{"id":35846,"date":"2022-04-03T13:02:19","date_gmt":"2022-04-03T07:32:19","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=35846"},"modified":"2022-04-07T11:11:50","modified_gmt":"2022-04-07T05:41:50","slug":"big-ideas-math-geometry-answers-chapter-2","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers-chapter-2\/","title":{"rendered":"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs"},"content":{"rendered":"<p>Reasoning and Proofs Chapter Answers provided are aligned as per the Big Ideas Math Geometry Textbooks. Have an overview of the concepts you need to learn in BIM Geometry Ch 2 Reasoning and Proofs and test your understanding. Master the topics of BIM Geometry Chapter 2 Reasoning and Proofs by practicing from the quick links available below. Identify the knowledge gap and concentrate on the areas you are lagging and improvise on them accordingly. You will find the <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-geometry-answers\/\">Big Ideas Math Geometry Answers<\/a> and attempt the exam with utmost confidence.<\/p>\n<h2>Big Ideas Math Book Geometry Answer Key Chapter 2 Reasoning and Proofs<\/h2>\n<p>Become proficient in the concepts of BIM Geometry Chapter 2 Reasoning and Proofs by referring to the quick links available. Solve the Questions available in BIM Book Geometry Chapter 2 Reasoning and Proofs Answer Key on a frequent basis and get a good hold of the concepts. Geometry Big Ideas Math Chapter 2 Reasoning and Proofs Answers here include questions from Lessons, Review Tests, Cumulative Practice, Assessment Tests, Practice Tests, etc. aligned as per the Textbooks. Download the Big Ideas Math Book Geometry Ch 2 Reasoning and Proofs Solution Key for free of cost and ace your preparation.<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Reasoning_and_Proofs_Maintaining_Mathematical_Proficiency\">Reasoning and Proofs Maintaining Mathematical Proficiency &#8211; Page 63<\/a><\/li>\n<li><a href=\"#Reasoning_and_Proofs_Mathematical_Practices\">Reasoning and Proofs Mathematical Practices &#8211; Page 64<\/a><\/li>\n<li><a href=\"#2.1_Conditional_Statements\">2.1 Conditional Statements &#8211; Page(65-74)<\/a><\/li>\n<li><a href=\"#Lesson_2.1_Conditional_Statements\">Lesson 2.1 Conditional Statements &#8211; Page(66-70)<\/a><\/li>\n<li><a href=\"#Exercise_2.1_Conditional_Statements\">Exercise 2.1 Conditional Statements &#8211; Page(71-74)<\/a><\/li>\n<li><a href=\"#2.2_Inductive_and_Deductive_Reasoning\">2.2 Inductive and Deductive Reasoning &#8211; Page(75-82)<\/a><\/li>\n<li><a href=\"#Lesson_2.2_Inductive_and_Deductive_Reasoning\">Lesson 2.2 Inductive and Deductive Reasoning &#8211; Page(76-79)<\/a><\/li>\n<li><a href=\"#Exercise_2.2_Inductive_and_Deductive_Reasoning\">Exercise 2.2 Inductive and Deductive Reasoning &#8211; Page(80-82)<\/a><\/li>\n<li><a href=\"#2.3_Postulates_and_Diagrams\">2.3 Postulates and Diagrams &#8211; Page(83-88)<\/a><\/li>\n<li><a href=\"#Lesson_2.3_Postulates_and_Diagrams\">Lesson 2.3 Postulates and Diagrams &#8211; Page(84-86)<\/a><\/li>\n<li><a href=\"#Exercise_2.3_Postulates_and_Diagrams\">Exercise 2.3 Postulates and Diagrams &#8211; Page(87-88)<\/a><\/li>\n<li><a href=\"#2.1_-_2.3_Study_Skills:_Using_the_Features_of_Your_Textbook_to_Prepare_for_Quizzes_and_Tests\">2.1 &#8211; 2.3 Study Skills: Using the Features of Your Textbook to Prepare for Quizzes and Tests &#8211; Page 89<\/a><\/li>\n<li><a href=\"#2.1_-_2.3_Quiz\">2.1 &#8211; 2.3 Quiz &#8211; Page 90<\/a><\/li>\n<li><a href=\"#2.4_Algebraic_Reasoning\">2.4 Algebraic Reasoning &#8211; Page(91-98)<\/a><\/li>\n<li><a href=\"#Lesson_2.4_Algebraic_Reasoning\">Lesson 2.4 Algebraic Reasoning &#8211; Page(92-95)<\/a><\/li>\n<li><a href=\"#Exercise_2.4_Algebraic_Reasoning\">Exercise 2.4 Algebraic Reasoning &#8211; Page(96-98)<\/a><\/li>\n<li><a href=\"#2.5_Proving_Statements_about_Segments_and_Angles\">2.5 Proving Statements about Segments and Angles &#8211; Page(99-104)<\/a><\/li>\n<li><a href=\"#Lesson_2.5_Proving_Statements_about_Segments_and_Angles\">Lesson 2.5 Proving Statements about Segments and Angles &#8211; Page(100-102)<\/a><\/li>\n<li><a href=\"#Exercise_2.5_Proving_Statements_about_Segments_and_Angles\">Exercise 2.5 Proving Statements about Segments and Angles &#8211; Page(103-104)<\/a><\/li>\n<li><a href=\"#2.6_Proving_Geometric_Relationships\">2.6 Proving Geometric Relationships &#8211; Page 105<\/a><\/li>\n<li><a href=\"#Lesson_2.6_Proving_Geometric_Relationships\">Lesson 2.6 Proving Geometric Relationships &#8211; Page(106-114)<\/a><\/li>\n<li><a href=\"#Exercise_2.6_Proving_Geometric_Relationships\">Exercise 2.6 Proving Geometric Relationships &#8211; Page(111-114)<\/a><\/li>\n<li><a href=\"#2.4_-_2.6_Performance_Task:_Induction_and_the_Next_Dimension\">2.4 &#8211; 2.6 Performance Task: Induction and the Next Dimension &#8211; Page 115<\/a><\/li>\n<li><a href=\"#Reasoning_and_Proofs_Chapter_Review\">Reasoning and Proofs Chapter Review &#8211; Page(116-118)<\/a><\/li>\n<li><a href=\"#Reasoning_and_Proofs_Test\">Reasoning and Proofs Test &#8211; Page 119<\/a><\/li>\n<li><a href=\"#Reasoning_and_Proofs_Cumulative_Assessment\">Reasoning and Proofs Cumulative Assessment &#8211; Page(120-121)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><a id=\"Reasoning_and_Proofs_Maintaining_Mathematical_Proficiency\"><\/a>Reasoning and Proofs Maintaining Mathematical Proficiency<\/h3>\n<p>Write an equation for the nth term of the arithmetic sequence. Then find a<sub>50<\/sub>.<\/p>\n<p>Question 1.<br \/>\n3, 9, 15, 21, &#8230;&#8230;..<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n&#8211; 29, &#8211; 12, 5, 22, &#8230;&#8230;..<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n2.8, 3.4, 4.0, 4.6, &#8230;&#8230;&#8230;<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{1}{3}, \\frac{1}{2}, \\frac{2}{3}, \\frac{5}{6}\\), &#8230;&#8230;&#8230;<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n26, 22, 18, 14, &#8230;&#8230;&#8230;<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n8, 2, &#8211; 4, &#8211; 10, &#8230;&#8230;&#8230;<br \/>\nAnswer:<\/p>\n<p>Solve the literal equation for x.<\/p>\n<p>Question 7.<br \/>\n2y &#8211; 2x = 10<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n20y + 5x = 15<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n4y &#8211; 5 = 4x + 7<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\ny = 8x &#8211; x<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ny = 4x + zx + 6<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nz = 2x + 6xy<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nCan you use the equation for an arithmetic sequence to write an equation for the sequence 3, 9, 27, 81. . . . ? Explain our reasoning.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Reasoning_and_Proofs_Mathematical_Practices\"><\/a>Reasoning and Proofs Mathematical Practices<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Decide whether the syllogism represents correct or flawed reasoning, If flawed, explain why the conclusion Is not valid.<\/p>\n<p>Question 1.<br \/>\nAll triangles are polygons.<br \/>\nFigure ABC is a triangle.<br \/>\nTherefore, figure ABC is a polygon.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nNo trapezoids are rectangles.<br \/>\nSome rectangles are not squares.<br \/>\nTherefore, some squares are not trapezoids.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nIf polygon ABCD is a square. then ills a rectangle.<br \/>\nPolygon ABCD is a rectangle.<br \/>\nTherefore, polygon ABCD is a square.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIf polygon ABCD is a square, then it is a rectangle.<br \/>\nPolygon ABCD is not a square.<br \/>\nTherefore, polygon ABCD is not a rectangle.<br \/>\nAnswer:<\/p>\n<h3><a id=\"2.1_Conditional_Statements\"><\/a>2.1 Conditional Statements<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Determining Whether a Statement is True or False<\/p>\n<p>Work with a partner: A hypothesis can either be true or false. The same is true of a conclusion. For a conditional statement to be true, the hypothesis and conclusion do not necessarily both have to be true. Determine whether each conditional statement is true or false. Justify your answer.<\/p>\n<p>a. If yesterday was Wednesday, then today is Thursday.<br \/>\nAnswer:<\/p>\n<p>b. If an angle is acute. then it has a measure of 30\u00b0.<br \/>\nAnswer:<\/p>\n<p>c. If a month has 30 days. then it is June.<br \/>\nAnswer:<\/p>\n<p>d. If an even number is not divisible by 2. then 9 is a perfect cube.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Determining Whether a Statement is True or False<\/p>\n<p>Work with a partner: Use the points in the coordinate plane to determine whether each statement is true or false. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 1\" width=\"241\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-1.png 241w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-1-150x150.png 150w\" sizes=\"(max-width: 241px) 100vw, 241px\" \/><br \/>\na. \u2206ABC is a right triangle.<br \/>\nAnswer:<\/p>\n<p>b. \u2206BDC is an equilateral triangle.<br \/>\nAnswer:<\/p>\n<p>c. \u2206BDC is an isosceles triangle.<br \/>\nAnswer:<\/p>\n<p>d. Quadrilateral ABCD is a trapezoid.<br \/>\nAnswer:<\/p>\n<p>e. Quadrilateral ABCD is a parallelogram.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 3<\/strong><\/p>\n<p>Determining Whether a Statement is True or False<\/p>\n<p>Work with a partner: Determine whether each conditional statement is true or false. Justify your answer.<\/p>\n<p><strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to distinguish correct logic or reasoning from that which is flawed.<\/p>\n<p>a. If \u2206 ADC is a right triangle, then the Pythagorean Theorem is valid for \u2206ADC.<br \/>\nAnswer:<\/p>\n<p>b. If \u2220A and \u2220B are complementary, then the sum of their measures is 180\u00b0.<br \/>\nAnswer:<\/p>\n<p>c. If figure ABCD is a quadrilateral, then the sum of its angle measures is 180\u00b0.<br \/>\nAnswer:<\/p>\n<p>d. If points A, B, and C are collinear, then the lie on the same line.<br \/>\nAnswer:<\/p>\n<p>e. It <img loading=\"lazy\" class=\"alignnone size-full wp-image-35926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2\" width=\"33\" height=\"23\" \/> and <img loading=\"lazy\" class=\"alignnone size-full wp-image-35925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 3\" width=\"34\" height=\"22\" \/> intersect at a point, then they form two pairs of vertical angles.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Communicate_Your_Answer\"><\/a>Communicate Your Answer<\/h3>\n<p>Question 4.<br \/>\nWhen is a conditional statement true or false?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWrite one true conditional statement and one false conditional statement that are different from those given in Exploration 3. Justify your answer.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_2.1_Conditional_Statements\"><\/a>Lesson 2.1 Conditional Statements<\/h3>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Use red to identify the hypothesis and blue to identify the conclusion. Then<br \/>\nrewrite the conditional statement in if-then form.<\/p>\n<p>Question 1.<br \/>\nAll 30\u00b0 angles are acute angles.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n2x + 7 = 1. because x = &#8211; 3.<br \/>\nAnswer:<\/p>\n<p>In Exercises 3 and 4, write the negation of the statement.<\/p>\n<p>Question 3.<br \/>\nThe shirt is green.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe Shoes are not red.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nRepeat Example 3. Let p be &#8220;the stars are visible\u201d and let q be &#8220;it is night.\u201d<br \/>\nAnswer:<\/p>\n<p>Use the diagram. Decide whether the statement is true. Explain your answer using the definitions you have learned.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-4.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 4\" width=\"208\" height=\"100\" \/><\/p>\n<p>Question 6.<br \/>\n\u2220JMF and \u2220FMG are supplementary.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nPoint M is the midpoint of \\(\\overline{F H}\\).<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\u2220JMF and \u2220HMG arc vertical angles.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 5\" width=\"75\" height=\"30\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nRewrite the definition of a right angle as a single biconditional statement.<br \/>\nDefinition: If an angle is a right angle. then its measure is 90\u00b0.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nRewrite the definition of congruent segments as a single biconditional statement.<br \/>\nDefinition: If two line segments have the same length. then they are congruent segments.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nRewrite the statements as a single biconditional statement.<br \/>\nIf Mary is in theater class, then she will be in the fall play. If Mary is in the fall play. then she must be taking theater class.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nRewrite the statements as a single biconditional statement.<br \/>\nIf you can run for President. then you are at least 35 years old. If you are at least 35 years old. then you can run for President.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nMake a truth table for the conditional statement p \u2192 ~ q.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nMake a truth table for the conditional statement ~(p \u2192 q).<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_2.1_Conditional_Statements\"><\/a>Exercise 2.1 Conditional Statements<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat type of statements are either both true or both false?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 1\" width=\"564\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-1.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-1-300x45.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich statement does not belong with the other three? Explain your reasoning.<br \/>\nIf today is Tuesday, then tomorrow is Wednesday<br \/>\nIf it is Independence Day, then it is July.<br \/>\nIf an angle is acute. then its measure is less than 90\u00b0.<br \/>\nIf you are an athlete, then you play soccer.<br \/>\nAnswer:<\/p>\n<p>In Exercises 3 &#8211; 6. copy the conditional statement. Underline the hypothesis and circle the conclusion.<\/p>\n<p>Question 3.<br \/>\nIf a polygon is a pentagon, then it has five sides.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 3\" width=\"364\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-3.png 364w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-3-300x50.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>Question 4.<br \/>\nIf two lines form vertical angles, then they intersect.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nIf you run, then you are fast.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 5\" width=\"246\" height=\"62\" \/><\/p>\n<p>Question 6.<br \/>\nIf you like math. then you like science.<br \/>\nAnswer:<\/p>\n<p>In Exercises 7 &#8211; 12. rewrite the conditional statement in if-then form.<\/p>\n<p>Question 7.<br \/>\n9x + 5 = 23, because x = 2.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 7\" width=\"258\" height=\"36\" \/><\/p>\n<p>Question 8.<br \/>\nToday is Friday, and tomorrow is the weekend.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nYou are in a hand. and you play the drums.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 9\" width=\"422\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-9.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-9-300x23.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 10.<br \/>\nTwo right angles are supplementary angles.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nOnly people who are registered are allowed to vote.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 11\" width=\"460\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-11.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-11-300x24.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>Question 12.<br \/>\nThe measures complementary angles sum to 90\u00b0<br \/>\nAnswer:<\/p>\n<p>In Exercises 13 &#8211; 16. write the negation of the statement.<\/p>\n<p>Question 13.<br \/>\nThe sky is blue.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 13\" width=\"190\" height=\"36\" \/><\/p>\n<p>Question 14.<br \/>\nThe lake is cold.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nThe ball is not pink.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 15\" width=\"159\" height=\"34\" \/><\/p>\n<p>Question 16.<br \/>\nThe dog is not a Lab.<br \/>\nAnswer:<\/p>\n<p>In Exercises 17 &#8211; 24. write the conditional statement p \u2192 q. the converse q \u2192 p, the inverse ~ p \u2192 ~ q, and the contrapositive ~ q \u2192 ~ p in words. Then decide whether each statement is true or false.<\/p>\n<p>Question 17.<br \/>\nLet p be \u201ctwo angles are supplementary\u201d and let q be \u201cthe measures of the angles sum to 180\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 17\" width=\"586\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-17.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-17-300x125.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 18.<br \/>\nLet p be \u201cyou are in math class\u201d and let q be \u201cyou are in Geometry:\u201d<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nLet p be &#8220;you do your math homework\u201d and let q be \u201cyou will do well on the test.\u201d<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 19\" width=\"588\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-19.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-19-300x126.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 20.<br \/>\nLet p be \u201cyou are not an only child\u201d and let q be \u201cyou have a sibling.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nLet p be \u201cit does not snow\u201d and let q be I will run outside.\u201d<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 21\" width=\"555\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-21.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-21-300x102.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 22.<br \/>\nLet p be \u201cthe Sun is out\u201d and let q be \u201cit is day time\u201d<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nLet p be \u201c3x &#8211; 7 = 20\u201d and let q be \u201cx = 9.\u201d<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 23\" width=\"532\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-23.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-23-300x78.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 24.<br \/>\nLet p be \u201cit is Valentine\u2019s Day\u201d and let q be \u201cit is February.<br \/>\nAnswer:<\/p>\n<p>In Exercises 25 &#8211; 28, decide whether the statement about the diagram is true. Explain your answer using the definitions you have learned.<\/p>\n<p>Question 25.<br \/>\nm\u2220ABC = 90\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-6.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 6\" width=\"125\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 25\" width=\"534\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-25.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-25-300x31.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 7\" width=\"74\" height=\"31\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-8.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 8\" width=\"142\" height=\"114\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nm\u22202 + m\u22203 = 180\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 9\" width=\"183\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 27\" width=\"571\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-27.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-27-300x30.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 28.<br \/>\nM is the midpoint of \\(\\overline{A B}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-10.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 10\" width=\"150\" height=\"32\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 29 &#8211; 32. rewrite the definition of the term as a biconditional statement.<\/p>\n<p>Question 29.<br \/>\nThe midpoint of a segment is the point that divides the segment into two congruent segments.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 29\" width=\"555\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-29.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-29-300x31.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 30.<br \/>\nTwo angles are vertical angles when their sides form two pairs of opposite rays.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nAdjacent angles are two angles that share a common vertex and side but have no common interior points.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 31\" width=\"553\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-31.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-31-300x31.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 32.<br \/>\nTwo angles are supplementary angles when the sum of their measures 180\u00b0.<br \/>\nAnswer:<\/p>\n<p>In Exercises 33 &#8211; 36. rewrite the statements as a single biconditional statement.<\/p>\n<p>Question 33.<br \/>\nIf a polygon has three sides. then it is a triangle.<br \/>\nIf a polygon is a triangle, then it has three sides.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 33\" width=\"508\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-33.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-33-300x20.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p>Question 34.<br \/>\nIf a polygon has four sides, then it is a quadrilateral.<br \/>\nIf a polygon is a quadrilateral, then it has four sides.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nIf an angle is a right angle. then it measures 90\u00b0.<br \/>\nIf an angle measures 90\u00b0. then it is a right angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 35\" width=\"560\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-35.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-35-300x17.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 36.<br \/>\nIf an angle is obtuse, then ii has a measure between 90\u00b0 and 180\u00b0.<br \/>\nIf an angle has a measure between 90\u00b0 and 180\u00b0. then it is obtuse.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in rewriting the conditional statement in if &#8211; then form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 11\" width=\"292\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 37\" width=\"588\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-37.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-37-300x73.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in writing the converse of the conditional statement.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-12.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 12\" width=\"287\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 39 &#8211; 44. create a truth table for the logical statement.<br \/>\nQuestion 39.<br \/>\n~ p \u2192 q<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 39\" width=\"283\" height=\"204\" \/><\/p>\n<p>Question 40.<br \/>\n~ q \u2192 p<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n~(~ p \u2192 ~ q)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 41\" width=\"468\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-41.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-41-300x130.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 42.<br \/>\n~ (p \u2192 ~ q)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nq \u2192 ~ p<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 43\" width=\"276\" height=\"203\" \/><\/p>\n<p>Question 44.<br \/>\n~ (q \u2192 p)<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nThe statements below describe three ways that rocks are formed.<\/p>\n<p>Igneous rock is formed from the cooling of Molten rock.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 13\" width=\"134\" height=\"114\" \/><\/p>\n<p>Sedimentary rock is formed from pieces of other rocks.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-14.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 14\" width=\"156\" height=\"113\" \/><\/p>\n<p>Metamorphic rock is formed by changing, temperature, pressure, or chemistry.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 15\" width=\"153\" height=\"120\" \/><\/p>\n<p>a. Write each sLaternenl in if-then form.<br \/>\nb. Write the converse of each of the statements in part (a). Is the converse of each statement true? Explain your reasoning.<br \/>\nc. Write a true if-then statement about rocks that is different from the ones in parts (a) and (b). Is the converse of our statement true or false? Explain your reasoning<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-45.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 45.1\" width=\"592\" height=\"466\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-45.1.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-45.1-300x236.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-45.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 45.2\" width=\"577\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-45.2.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-45.2-300x105.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims the statement \u201cIf I bought a shirt, then I went to the mall\u2019 can he written as a true biconditional statement. Your sister says you cannot write it as a biconditional. Who is correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are told that the contrapositive of a statement is true. Will that help you determine whether the statement can be written as a true biconditional statement\u2019? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-47.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 47\" width=\"575\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-47.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-47-300x57.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nUse the conditional statement to identify the if-then statement as the converse. inverse. or contrapositive of the conditional statement. Then use the symbols to represent both statements.<br \/>\nConditional statement: It I rode my bike to school, then I did not walk to school.<br \/>\nIf-then statement: If did not ride my bike to school, then I walked to school.<br \/>\np\u00a0 \u00a0 \u00a0 q\u00a0 \u00a0 \u00a0~\u00a0 \u00a0 \u2192\u00a0 \u00a0 \u2194<br \/>\nAnswer:<\/p>\n<p><strong>USING STRUCTURE<\/strong><br \/>\nIn Exercises 49 &#8211; 52. rewrite the conditional statement in if-then form. Then underline the hypothesis and circle the conclusion.<br \/>\nQuestion 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-16.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 16\" width=\"188\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-49.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 49\" width=\"499\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-49.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-49-300x78.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 17\" width=\"189\" height=\"120\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-18.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 18\" width=\"177\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-51.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 51\" width=\"583\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-51.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-51-300x80.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 19\" width=\"173\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nCan the statement \u201cIf x<sup>2<\/sup> &#8211; 10 = x + 2. then x = 4&#8243; be combined with its converse to form a true biconditional statement?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-53.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 53\" width=\"530\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-53.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-53-300x79.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe largest natural arch in the United States is Landscape Arch. located in Thompson, Utah. h spans 290 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-20.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 20\" width=\"317\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-20.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-20-300x246.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\na. Use the information to write at least two true conditional statements.<br \/>\nAnswer:<\/p>\n<p>b. Which type of related conditional statement must also be true? Write the related conditional statements.<br \/>\nAnswer:<\/p>\n<p>C. What are the other two types of related conditional statements? Write the related conditional statements. Then determine their truth values. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich statement has the same meaning as the given statement?<br \/>\nGiven statement:<br \/>\nYou can watch a movie after you do your homework.<br \/>\n(A) If you do your homework, then you can watch a movie afterward.<br \/>\n(B) If you do not do your homework, then you can watch a movie afterward.<br \/>\n(C) If you cannot watch a movie afterward. then do your homework.<br \/>\n(D) If you can watch a movie afterward, then do not do your homework.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-55.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 55\" width=\"548\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-55.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-55-300x47.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite three conditional statements. where one is always true, one is always false, and one depends on the person interpreting the statement.<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nOne example of a conditional statement involving dates is \u201cIf today is August 31, then tomorrow is September 1 Write a conditional statement using dates from two different months so that the truth value depends on when the statement is read.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-57.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 57\" width=\"486\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-57.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-57-300x20.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe Venn diagram represents all the musicians at a high school. Write three conditional statements in if-then form describing the relationships between the various groups of musicians.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 21\" width=\"342\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-21.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-21-300x125.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nCreate a Venn diagram representing each conditional statement. Write the converse of each conditional statement. Then determine whether each conditional statement and its converse are true or false. Explain your reasoning.<br \/>\na. If you go to the zoo to see a lion, then you will see a Cat.<br \/>\nb. If you play a sport. then you wear a helmet.<br \/>\nc. If this month has 31 days. then it is not February.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-59.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 59.1\" width=\"654\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-59.1.png 654w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-59.1-300x154.png 300w\" sizes=\"(max-width: 654px) 100vw, 654px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-59.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 59.2\" width=\"692\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-59.2.png 692w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-59.2-300x229.png 300w\" sizes=\"(max-width: 692px) 100vw, 692px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nYou measure the heights of your classmates to gel a data set.<br \/>\na. Tell whether this statement is true: If s and y are the least and greatest values in your data set, then the mean of the data is between x and y.<br \/>\nAnswer:<\/p>\n<p>b. Write the converse of the statement in part (a). Is the converse true? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>c. Copy and complete the statement below using mean, median, or mode to make a conditional statement that is true for an data set. Explain your reasoning.<br \/>\nIf a data set has a mean. median, and a mode. then the _____________ of the data set will always be a data value.<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<strong>WRITING<\/strong><br \/>\nWrite a conditional statement that is true, but its converse is false.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-61.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 61\" width=\"574\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-61.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-61-300x83.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nwrite a series of if-then statements that allow you to find the measure of each angle, given that m\u22201 = 90\u00b0 Use the definition of linear pairs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-22.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 22\" width=\"126\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<strong>WRITING<\/strong><br \/>\nAdvertising slogans such as &#8220;Buy these shoes! They will make you a better athlete!\u201d often imply conditional statements. Find an advertisement or write your own slogan. Then write it as a conditional statement.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-63.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 63\" width=\"576\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-63.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-63-300x67.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p>Find the pattern. Then draw the next two figures in the sequence.<\/p>\n<p>Question 64.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 23\" width=\"449\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-23.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-23-300x51.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-24.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 24\" width=\"327\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-24.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-24-300x75.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-65.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 65\" width=\"563\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-65.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-65-300x94.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Find the pattern. Then write the next two numbers.<\/p>\n<p>Question 66.<br \/>\n1, 3, 5, 7 &#8230;&#8230;..<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n12, 23, 34, 45 &#8230;&#8230;..<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-67.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 67\" width=\"487\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-67.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-67-300x171.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 68.<br \/>\n2, \\(\\frac{4}{3}, \\frac{8}{9}, \\frac{16}{27}\\), &#8230;&#8230;..<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n1, 4, 9, 16, &#8230;&#8230;..<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-69.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.1 Question 69\" width=\"480\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-69.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.1-Question-69-300x174.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<h3><a id=\"2.2_Inductive_and_Deductive_Reasoning\"><\/a>2.2 Inductive and Deductive Reasoning<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing a Conjecture<\/p>\n<p>Work with a partner: Write a conjecture about the pattern. Then use your conjecture to draw the 10th object in the pattern.<br \/>\na.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-25.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 25\" width=\"512\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-25.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-25-300x55.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><br \/>\nAnswer:<\/p>\n<p>b.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-26.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 26\" width=\"498\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-26.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-26-300x38.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\nAnswer:<\/p>\n<p>c.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-27.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 27\" width=\"499\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-27.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-27-300x38.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Using a Venn Diagram<\/p>\n<p>Work with a partner: Use the Venn diagram to determine whether the statement is true or false. Justify your answer. Assume that no region of the Venn diagram is empty.<\/p>\n<p><strong>CONSTRUCTING VIABLE ARGUMENTS<\/strong><br \/>\nTo be proficient in math, you need to justify your conclusions and communicate them to others.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-28.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 28\" width=\"289\" height=\"148\" \/><\/p>\n<p>a. If an item has Property B. then it has Property A.<br \/>\nAnswer:<\/p>\n<p>b. If an item has Property A. then it has Property B.<br \/>\nAnswer:<\/p>\n<p>c. If an item has Property A, then it has Property C.<br \/>\nAnswer:<\/p>\n<p>d. Some items that have Property A do not have Property B.<br \/>\nAnswer:<\/p>\n<p>e. If an item has Property C. then it does not have Property B.<br \/>\nAnswer:<\/p>\n<p>f. Sonic items have both Properties A and C.<br \/>\nAnswer:<\/p>\n<p>g. Some items have both Properties B and C.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 3<\/strong><\/p>\n<p>Reasoning and Venn Diagrams<\/p>\n<p>Work with a partner: Draw a Venn diagram that shows the relationship between different types of quadrilateral: squares. rectangles. parallelograms. trapezoids. rhombuses, and kites. Then write several conditional statements that are shown in your diagram. such as \u201cIf a quadrilateral is a square. then it is a rectangle.\u201d<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 4.<br \/>\nHow can you use reasoning to solve problems?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nGive an example of how you used reasoning to solve a real-life problem.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_2.2_Inductive_and_Deductive_Reasoning\"><\/a>Lesson 2.2 Inductive and Deductive Reasoning<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nSketch the fifth figure in the pattern in Example 1.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-29.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 29\" width=\"344\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-29.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-29-300x90.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-30.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 30\" width=\"268\" height=\"53\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nMake and test a conjecture about the sign o1 the product of any three negative integers.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nMake and test a conjecture about the sum of any five consecutive integers.<br \/>\nAnswer:<\/p>\n<p>Find a counterexample to show that the conjecture is false.<\/p>\n<p>Question 6.<br \/>\nThe value of x<sup>2<\/sup> is always greater than the value of x.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nThe sum of two numbers is always greater than their difference.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nIf 90\u00b0 \u2220 m \u2220 R \u2220 180\u00b0, then \u2220R is obtuse. The measure of \u2220R is 155\u00b0. Using the Law of Detachment. what statement can you make?<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nUse the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.<br \/>\nIf you get an A on your math test. then you can go to the movies.<br \/>\nIf you go to the movies, then you can watch your favorite actor.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nUse inductive reasoning to make a conjecture about the sum of a number and itself. Then use deductive reasoning to show that the conjecture is true.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nDecide whether inductive reasoning or deductive reasoning is used to reach the<br \/>\nconclusion. Explain your reasoning.<br \/>\nAll multiples of 8 are divisible by 4.<br \/>\n64 is a multiple of 8.<br \/>\nSo, 64 is divisible by 4.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_2.2_Inductive_and_Deductive_Reasoning\"><\/a>Exercise 2.2 Inductive and Deductive Reasoning<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow does the prefix \u201ccounter\u201d help you understand the term counterexample?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 1\" width=\"474\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-1.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-1-300x37.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain the difference between inductive reasoning and deductive reasoning.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 &#8211; 8, describe the pattern. Then write or draw the next two numbers, letters, or figures.<\/p>\n<p>Question 3.<br \/>\n1, &#8211; 2, 3, &#8211; 4, 5, &#8230;&#8230;..<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 3\" width=\"573\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-3.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-3-300x57.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 4.<br \/>\n0, 2, 6, 12, 20, &#8230;&#8230;..<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nZ, Y, X, W, V, &#8230;&#8230;..<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 5\" width=\"551\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-5.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-5-300x30.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 6.<br \/>\nJ, F, M, A, M, &#8230;&#8230;..<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-31.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 31\" width=\"206\" height=\"57\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 7\" width=\"587\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-7.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-7-300x93.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-32.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 32\" width=\"217\" height=\"74\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 9 &#8211; 12. make and test a conjecture about the given quantity.<\/p>\n<p>Question 9.<br \/>\nthe product of any two even integers<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 9\" width=\"519\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-9.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-9-300x36.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 10.<br \/>\nthe sum of an even integer and an odd integer<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nthe quotient of a number and its reciprocal<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 11\" width=\"556\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-11.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-11-300x125.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 12.<br \/>\nthe quotient of two negative integers<br \/>\nAnswer:<\/p>\n<p>In Exercises 13 &#8211; 16, find a counter example to show that the conjecture is false.<\/p>\n<p>Question 13.<br \/>\nThe product of two positive numbers is always greater than either number,<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 13\" width=\"545\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-13.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-13-300x78.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 14.<br \/>\nIf n is a nonzero integer, then \\(\\frac{n+1}{n}\\) is always greater than 1.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nIf two angles are supplements of each other. then one of the angles must be acute.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 15\" width=\"451\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-15.png 451w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-15-300x23.png 300w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p>Question 16.<br \/>\nA line s divides \\(\\overline{M N}\\) into two line segments. So, the lines is a segment bisector of \\(\\overline{M N}\\)<br \/>\nAnswer:<\/p>\n<p>In Exercises 17 &#8211; 20. use the Law of Detachment to determine what you can conclude from the given information, if possible.<\/p>\n<p>Question 17.<br \/>\nIf you pass the final, then you pass the class. You passed the final.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 17\" width=\"207\" height=\"33\" \/><\/p>\n<p>Question 18.<br \/>\nIf your parents let you borrow the ear, then you will go to the movies with your friend. you will go to the movies with your friend.<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nIf a quadrilateral is a square. then it has four right angles. Quadrilateral QRST has four right angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 19\" width=\"376\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-19.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-19-300x28.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Question 20.<br \/>\nIf a point divides a line segment into two congruent line segments. then the point is a midpoint. Point P divides \\(\\overline{L H}\\) into two congruent line segments.<br \/>\nAnswer:<\/p>\n<p>In Exercises 21 &#8211; 24, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.<\/p>\n<p>Question 21.<br \/>\nIf x &lt; &#8211; 2, then |x| &gt; 2. If x &gt; 2. then |x| &gt; 2.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 21\" width=\"132\" height=\"32\" \/><\/p>\n<p>Question 22.<br \/>\nIf a = 3. then 5a = 15. If \\(\\frac{1}{2}\\)a = 1\\(\\frac{1}{2}\\), then a = 3.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nIf a figure is a rhombus then the figure is a parallelogram. If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 23\" width=\"517\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-23.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-23-300x35.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 24.<br \/>\nIf a figure is a square, then the figure has four congruent sides. If a figure is a square, then the figure has tour right angles.<br \/>\nAnswer:<\/p>\n<p>In Exercises 25 &#8211; 28. state the law of logic that is illustrated.<\/p>\n<p>Question 25.<br \/>\nIf you do your homework, then you can watch TV If you watch TV, then you can watch your favorite show.<br \/>\nIf you do your homework. then you can watch your favorite show.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 25\" width=\"444\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-25.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-25-300x26.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Question 26.<br \/>\nIf you miss practice the day before a game. then you will not be a starting player in the game.<br \/>\nYou miss practice on Tuesday. You will not start the game Wednesday.<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nIf x &gt; 12, then x + 9 &gt; 20. The value of x is 14. So, x + 9 &gt; 20.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 27\" width=\"466\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-27.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-27-300x23.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 28.<br \/>\nIf \u22201 and \u22202 are vertical angles. then \u22201 \u2245\u22202.<br \/>\nIf \u22201 \u2245\u22202 then m\u22201 \u2245 m\u22202.<br \/>\nIf \u22201 and \u22202 are vertical angles. then m\u22201 = m\u22202.<br \/>\nAnswer:<\/p>\n<p>In Exercises 29 and 30, use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to show that the conjecture is true.<\/p>\n<p>Question 29.<br \/>\nthe sum of two odd integers<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 29\" width=\"584\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-29.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-29-300x129.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 30.<br \/>\nthe product of two odd integers<br \/>\nAnswer:<\/p>\n<p>In Exercises 31 &#8211; 34. decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain your reasoning.<\/p>\n<p>Question 31.<br \/>\nEach time your mom goes to the store. she buy s milk. So. the next time your mom goes to the store. she will buy milk.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 31\" width=\"588\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-31.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-31-300x33.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 32.<br \/>\nRational numbers can be written as fractions. Irrational numbers cannot be written as tractions. So. \\(\\frac{1}{2}\\) is a rational number<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nAll men are mortal. Mozart is a man. so Mozart is mortal.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 33\" width=\"581\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-33.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-33-300x29.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 34.<br \/>\nEach time you clean your room. you are allowed to go out with your friends. So, the next time you clean your room. you will be allowed to go out with your friends.<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 35 and 36, describe and correct the error in interpreting the statement.<\/p>\n<p>Question 35.<br \/>\nIf a figure is a rectangle. then the figure has four sides.<br \/>\nA trapezoid has four sides.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-33.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 33\" width=\"342\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-33.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-33-300x53.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 35\" width=\"581\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-35.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-35-300x58.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 36.<br \/>\nEach day, you get to school before your friend.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-34.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 34\" width=\"339\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-34.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-34-300x68.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe table Shows the average weights of several subspecies of tigers. What conjecture can you make about the relation between the weights of female tigers and the weights of male tigers? Explain our reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-35.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 35\" width=\"410\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-35.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-35-300x180.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 37\" width=\"553\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-37.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-37-300x47.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nDetermine whether you can make each conjecture from the graph. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-36.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 36\" width=\"331\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-36.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-36-300x196.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\na. More girls will participate in high school lacrosse in Year 8 than those who participated in Year 7.<br \/>\nAnswer:<\/p>\n<p>b. The number of girls participating in high school lacrosse will exceed the number of boys participating in high school lacrosse in Year 9.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nUse inductive reasoning to write a formula for the sum of the first n positive even integers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 39\" width=\"550\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-39.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-39-300x149.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nThe following are the first nine Fibonacci numbers.<br \/>\n1, 1, 2, 3, 5, 8, 13, 21, 34, &#8230;&#8230;.<br \/>\na. Make a conjecture about each of the Fibonacci numbers after the first two.<br \/>\nAnswer:<\/p>\n<p>b. Write the next three numbers in the pattern.<br \/>\nAnswer:<\/p>\n<p>c. Research to find a real-world example of this pattern.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nWhich argument is correct? Explain your reasoning.<br \/>\nArgument 1: If two angles measure 30\u00b0 and 60\u00b0 then the angles are complementary. \u22201 and \u22202 are complementary. So. m\u22201 = 30\u00b0 and m\u22202 = 60\u00b0<\/p>\n<p>Argument 2: If two angles measure 30\u00b0 and 60\u00b0. then the angles are complementary. The measure of \u22201 is 30\u00b0 and the measure of \u22202 is 60\u00b0. So, \u22201 and \u22202 are complementary.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 41\" width=\"555\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-41.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-41-300x32.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe first two terms of a sequence are \\(\\frac{1}{4}\\) and \\(\\frac{1}{2}\\) Describe three different possible Patterns for the sequence. List the first five terms for each sequence.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nUse the table to make a conjecture about the relationship between x and y. Then write an equation for y in terms of x. Use the equation to test your conjecture for other values of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-37.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 37\" width=\"266\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 43\" width=\"525\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-43.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-43-300x65.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>REASONING<\/strong><br \/>\nUse the pattern below. Each figure is made of squares that are 1 unit by 1 unit.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-38.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 38\" width=\"309\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-38.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-38-300x105.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\na. Find the perimeter of each figure. Describe the pattern of the perimeters.<br \/>\nAnswer:<\/p>\n<p>b. Predict the perimeter of the 20th figure.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nDecide whether each conclusion is valid. Explain your reasoning.<\/p>\n<ul>\n<li>Yellowstone is a national park in Wyoming.<\/li>\n<li>You and your Friend went camping at Yellowstone National Park.<\/li>\n<li>When you go camping. you go canoeing.<\/li>\n<li>If you go on a hike, your Friend goes with you.<\/li>\n<li>You go on a hike.<\/li>\n<li>There is a 3-mile-long trail near your campsite.<\/li>\n<\/ul>\n<p>a. You went camping in Wyoming.<br \/>\nb. Your Friend went canoeing.<br \/>\nc. Your friend went on a hike.<br \/>\nd. You and your Friend went on a hike on a 3-mile-long trail.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 45\" width=\"592\" height=\"357\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-45.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-45-300x181.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nGeologists use the Mohs&#8217; scale to determine a mineral\u2019s hardness. Using the scale. a mineral with a higher rating will leave a scratch on a mineral with a lower rating. Testing a mineral\u2019s hardness can help identify the mineral.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-39.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 39\" width=\"363\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-39.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-39-300x117.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\na. The four minerals are randomly labeled A, B, C, and D. Mineral A is scratched by Mineral B. Mineral C is scratched by all three of the other minerals. What can you conclude? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>b. What additional test(s) can you use to identify all the minerals in part (a)?<br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Determine which postulate is illustrated by the statement.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-40.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 40\" width=\"141\" height=\"107\" \/><\/p>\n<p>Question 47.<br \/>\nAB + BC = AC<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-47.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 47\" width=\"372\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-47.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-47-300x31.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/p>\n<p>Question 48.<br \/>\nm\u2220DAC = m\u2220DAE + m\u2220EAB<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nAD is the absolute value of the difference of the coordinates of A and D.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.2-Question-49.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.2 Question 49\" width=\"253\" height=\"33\" \/><\/p>\n<p>Question 50.<br \/>\nm\u2220DAC is equal to the absolute value of the difference between the real numbers matched with \\(\\vec{A}\\)D and \\(\\vec{A}\\)C on a protractor.<br \/>\nAnswer:<\/p>\n<h3><a id=\"2.3_Postulates_and_Diagrams\"><\/a>2.3 Postulates and Diagrams<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Looking at a Diagram<\/p>\n<p>Work with a partner. On a piece of paper. draw two perpendicular lines. Label them <img loading=\"lazy\" class=\"alignnone size-full wp-image-36151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-41.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 41\" width=\"32\" height=\"25\" \/> and <img loading=\"lazy\" class=\"alignnone size-full wp-image-36150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-42.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 42\" width=\"38\" height=\"28\" \/>. Look at the diagram from different angles. Do the lines appear perpendicular regardless of the angle at which you look at them? Describe all the angles at which you can l00k at the lines and have them appear perpendicular.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-43.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 43\" width=\"526\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-43.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-43-300x150.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Interpreting a Diagram<\/p>\n<p>Work with a partner: When you draw a diagram, you are communicating with others. It is important that you include sufficient information in the diagram. Use the diagram to determine which of the following statements you can assume to be true. Explain your reasoning.<\/p>\n<p><strong>ATTENDING TO PRECISION<\/strong><br \/>\nTo be proficient in math, you need to state the meanings of the symbols you choose.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-44.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 44\" width=\"238\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-44.png 238w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-44-150x150.png 150w\" sizes=\"(max-width: 238px) 100vw, 238px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-45.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 45\" width=\"275\" height=\"256\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-46.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 46\" width=\"235\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nIn a diagram, what can be assumed and what needs to be labeled?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse the diagram in Exploration 2 to write two statements you can assume to be true and two statements you cannot assume to be true. Your statements should be different from those given in Exploration 2. Explain our reasoning.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_2.3_Postulates_and_Diagrams\"><\/a>Lesson 2.3 Postulates and Diagrams<\/h3>\n<p><strong>Monitoring progress<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the diagram in Example 2. Which postulate allows you to say that the intersection of plane P and plane Q is a line?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nUse the diagram in Example 2 to write an example of the postulate.<br \/>\na. Two Point Postulate<br \/>\nAnswer:<\/p>\n<p>b. Line-Point Postulate<br \/>\nAnswer:<\/p>\n<p>c. Line Intersection Postulate<br \/>\nAnswer:<\/p>\n<p>Refer back to Example 3.<\/p>\n<p>Question 3.<br \/>\nIf the given information states that \\(\\overline{P W}\\) and \\(\\overline{Q W}\\) arc congruent. how can you indicate that in the diagram?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nName a pair of supplementary angles in the diagram. Explain.<br \/>\nAnswer:<\/p>\n<p>Use the diagram in Example 4.<\/p>\n<p>Question 5.<br \/>\nCan you assume that plane S intersects plane T at <img loading=\"lazy\" class=\"alignnone size-full wp-image-36145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-47.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 47\" width=\"34\" height=\"29\" \/>?<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nExplain how you know <img loading=\"lazy\" class=\"alignnone size-full wp-image-36144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-48.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 48\" width=\"75\" height=\"31\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_2.3_Postulates_and_Diagrams\"><\/a>Exercise 2.3 Postulates and Diagrams<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThrough any ___________ non collinear points. there exists exactly one plane.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 1\" width=\"579\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-1-300x31.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why you need at least three noncollinear points to determine a plane.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4. state the postulate illustrated by the diagram.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-49.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 49\" width=\"258\" height=\"94\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 3\" width=\"580\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-3.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-3-300x30.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-50.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 50\" width=\"328\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-50.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-50-300x54.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 5 &#8211; 8, use the diagram to write an example of the postulate.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-51.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 51\" width=\"322\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-51.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-51-300x78.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>Question 5.<br \/>\nLine-Point Postulate (Postulate 2.2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 5\" width=\"454\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-5.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-5-300x23.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Question 6.<br \/>\nLine Intersection Postulate (Postulate 2.3)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nThree Point Postulate (Postulate 2.4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 7\" width=\"552\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-7.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-7-300x32.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 8.<br \/>\nPlane-Line Postulate (Postulate 2.6)<br \/>\nAnswer:<\/p>\n<p>In Exercises 9 &#8211; 12. sketch a diagram of the description.<\/p>\n<p>Question 9.<br \/>\nplane P and line m intersection plane P at a 90\u00b0 angle<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 9\" width=\"406\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-9.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-9-300x151.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\overline{X Y}\\) in plane P, \\(\\overline{X Y}\\) bisected by point A. and point C not<br \/>\non \\(\\overline{X Y}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\overline{X Y}\\) intersecting \\(\\overline{W V}\\) at point A. so that XA = VA<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 11\" width=\"428\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-11.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-11-300x122.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\overline{A B}\\), \\(\\overline{C D}\\), and \\(\\overline{E F}\\) are all in plane P. and point x is the midpoint of all three segments.<br \/>\nAnswer:<\/p>\n<p>In Exercises 13 &#8211; 20, use the diagram to determine whether you can assume the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-52.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 52\" width=\"215\" height=\"145\" \/><\/p>\n<p>Question 13.<br \/>\nPlanes Wand X intersect at <img loading=\"lazy\" class=\"alignnone size-full wp-image-36139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-53.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 53\" width=\"31\" height=\"29\" \/>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 13\" width=\"341\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-13.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-13-300x33.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Question 14.<br \/>\nPoints K, L, M, and N are coplanar.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nPoints Q, J, and M are collinear.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 15\" width=\"577\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-15.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-15-300x46.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-54.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 54\" width=\"153\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-54.png 153w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-54-150x31.png 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-55.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 55\" width=\"32\" height=\"27\" \/> lies in plane X.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 17\" width=\"509\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-17.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-17-300x20.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p>Question 18.<br \/>\n\u2220PLK is a right angle.<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\u2220NKL and \u2220JKM are vertical angles.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 19\" width=\"397\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-19.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-19-300x27.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><\/p>\n<p>Question 20.<br \/>\n\u2220NKI and \u2220JKM are supplementary angles.<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 21 and 22. describe and correct the error in the statement made about the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-56.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 56\" width=\"141\" height=\"142\" \/><\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-57.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 57\" width=\"312\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-57.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-57-300x48.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 21\" width=\"572\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-21.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-21-300x78.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-58.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 58\" width=\"312\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-58.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-58-300x49.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nSelect all the statements about the diagram that you cannot conclude.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-59.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 59\" width=\"207\" height=\"199\" \/><br \/>\n(A) A, B, and C are coplanar.<br \/>\n<span style=\"font-size: 16px;\">(B) Plane T intersects plane S in <\/span><img loading=\"lazy\" class=\"alignnone size-full wp-image-36132\" style=\"font-style: inherit; font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-60.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 60\" width=\"35\" height=\"24\" \/><span style=\"font-size: 16px;\">.<br \/>\n<\/span><span style=\"font-size: 16px;\">(C) <\/span><img loading=\"lazy\" class=\"alignnone size-full wp-image-36131\" style=\"font-style: inherit; font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-61.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 61\" width=\"37\" height=\"24\" \/><span style=\"font-size: 16px;\"> intersects <\/span><img loading=\"lazy\" class=\"alignnone size-full wp-image-36130\" style=\"font-style: inherit; font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-62.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 62\" width=\"31\" height=\"25\" \/><span style=\"font-size: 16px;\">.<br \/>\n<\/span><span style=\"font-size: 16px;\">(D) H, F, and D are coplanar.<br \/>\n<\/span><span style=\"font-size: 16px;\">(E) Plane T \u22a5 plane S.<br \/>\n<\/span><span style=\"font-size: 16px;\">(F) Point B bisects \\(\\overline{H C}\\).<br \/>\n<\/span><span style=\"font-size: 16px;\">(G) \u2220ABH and \u2220HBF are a linear pair.<br \/>\n<\/span><span style=\"font-size: 16px;\">(H) <\/span><img loading=\"lazy\" class=\"alignnone size-full wp-image-36129\" style=\"font-style: inherit; font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-63.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 63\" width=\"80\" height=\"25\" \/><br \/>\n<span style=\"font-size: 16px;\">Answer:<\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 23\" width=\"555\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-23.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-23-300x16.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the diagram of line m and point C. Make a conjecture about how many planes can be drawn so that line m and point C lie in the same plane. Use postulates too justify your conjecture.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-64.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 64\" width=\"262\" height=\"58\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nOne way to graph a linear equation is to plot two points whose coordinates satisfy the equation and then connect them with a line. Which postulate guarantees this process works for any linear equation?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 25\" width=\"289\" height=\"35\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nA way to solve a system of two linear equations that intersect is to graph the lines and find the coordinates of their intersection. Which postulate guarantees this process works for an two linear equations?<br \/>\nAnswer:<\/p>\n<p>In Exercises 27 and 28, (a) rewrite the postulate in if-then form. Then (b) write the converse, inverse, and contrapositive and state which ones are true.<\/p>\n<p>Question 27.<br \/>\nTwo Point Postulate (Postulate 2.1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 27\" width=\"598\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-27.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-27-300x182.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 28.<br \/>\nPlane-Point Postulate (Postulate 2.5)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nChoose the correct symbol to go between the statements.<br \/>\n65<br \/>\n&lt;\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2264\u00a0 \u00a0 \u00a0 \u00a0 \u00a0=\u00a0 \u00a0 \u00a0 \u00a0 \u2265\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &gt;<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 29\" width=\"546\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-29.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-29-300x33.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIf two lines intersect, then they intersect in exactly one point by the Line Intersection Postulate (Postulate 2.3). Do the two lines have to be in the same plane ? Draw a picture to support your answer. Then explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that even though two planes intersect in a line, it is possible for three planes to intersect in a point. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 31\" width=\"536\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-31.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-31-300x154.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that by the Plane Intersection Postulate (Post. 2.7), any two planes intersect in a line. Is your friend\u2019s interpretation 0f the Plane Intersection Postulate (Post. 2.7) correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nPoints E, F, and G all lie in plane P and in plane Q. What must be true about points E, F. and G so that planes P and Q are different planes? What must be true about points E, F, and G to force planes P and Q to be the same plane? Make sketches to support your answers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 33\" width=\"598\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-33.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-33-300x130.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe postulates in this book represent Euclidean geometry. In spherical geometry. all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. A plane is the surface of the sphere. Find a postulate on page 84 that is not true in spherical geometry. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Solve the equation. Tell which algebraic property of equality you used.<\/p>\n<p>Question 35.<br \/>\nt &#8211; 6 = &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 35\" width=\"222\" height=\"179\" \/><\/p>\n<p>Question 36.<br \/>\n3x = 21<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n9 + x = 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.3-Question-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.3 Question 37\" width=\"208\" height=\"181\" \/><\/p>\n<p>Question 38.<br \/>\n\\(\\frac{x}{7}\\) = 5<br \/>\nAnswer:<\/p>\n<h3><a id=\"2.1_-_2.3_Study_Skills:_Using_the_Features_of_Your_Textbook_to_Prepare_for_Quizzes_and_Tests\"><\/a>2.1 &#8211; 2.3 Study Skills: Using the Features of Your Textbook to Prepare for Quizzes and Tests<\/h3>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nProvide a counter example for each false conditional statement in Exercises 17 &#8211; 24 on page 71.<br \/>\n(You do not need to consider the converse. inverse, and contrapositive statements.)<\/p>\n<p>Question 2.<br \/>\nCreate a truth table for each of your answers to Exercise 59 on page 74.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nFor Exercise 32 on page 88. write a question you would ask your friend about his or her interpretation.<br \/>\nAnswer:<\/p>\n<h3><a id=\"2.1_-_2.3_Quiz\"><\/a>2.1 &#8211; 2.3 Quiz<\/h3>\n<p>Rewrite the conditional statement in if-then form. Then write the converse, inverse, and contrapositive of the conditional statement. Decide whether each statement is true or false.<\/p>\n<p>Question 1.<br \/>\nAn angle measure of 167\u00b0 is an obtuse angle.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nYou are in a physics class, so you always have homework.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nI will take my driving test, So I will get my driver\u2019s license.<br \/>\nAnswer:<\/p>\n<p>Find a countereample to show that the conjecture is false.<\/p>\n<p>Question 4.<br \/>\nThe sum of a positive number and a negative number is always positive.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nIf a figure has four sides, then it is a rectangle.<br \/>\nAnswer:<\/p>\n<p>Use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to show that the conjecture is true.<\/p>\n<p>Question 6.<br \/>\nthe sum of two negative integers<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nthe difference of two even integers<br \/>\nAnswer:<\/p>\n<p>Use the diagram to determine whether you can assume the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-66.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 66\" width=\"242\" height=\"150\" \/><\/p>\n<p>Question 8.<br \/>\nPoints D, B, and C are coplanar.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nPlane EAF is parallel to plane DBC.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nLine m intersects line <img loading=\"lazy\" class=\"alignnone size-full wp-image-36162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-67.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 67\" width=\"32\" height=\"25\" \/> at point it.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nLine <img loading=\"lazy\" class=\"alignnone size-full wp-image-36161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-68.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 68\" width=\"39\" height=\"22\" \/> lies in plane DBC.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nm\u2220DBG = 90\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nYou and your friend are bowling. Your friend claims that the statement \u201cIf I got a strike, then I used thegreen ball\u201d can be written as a true biconditional statement. Is your friend correct? Explain your reasoning. (Section 2.1)<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nThe table shows the 1 &#8211; mile running times of the members of a high school track team.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-69.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 69\" width=\"263\" height=\"195\" \/><br \/>\na. What conjecture can you make about the running times of females and males?<br \/>\nAnswer:<\/p>\n<p>b. What type of reasoning did you use? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nList five of the seven Point, Line, and Plane Postulates on page 84 that the diagram of the house demonstrates. Explain how the postulate is demonstrated in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answer-Key-Chapter-2-Reasoning-and-Proofs-70.png\" alt=\"Big Ideas Math Geometry Answer Key Chapter 2 Reasoning and Proofs 70\" width=\"260\" height=\"223\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"2.4_Algebraic_Reasoning\"><\/a>2.4 Algebraic Reasoning<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Justifying steps in a solution<\/p>\n<p>Work with a partner: In previous courses. you studied di\u00edIrcnt properties. such as the properties of equality and the Distributive, Commutative, and Associative Properties. Write the property that justifies each of the following solution steps.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-69.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 69\" width=\"555\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-69.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-69-300x188.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Stating Algebraic Properties<\/p>\n<p>Work with a partner: The symbols <img loading=\"lazy\" class=\"alignnone size-full wp-image-36526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-70.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 70\" width=\"12\" height=\"18\" \/> and <img loading=\"lazy\" class=\"alignnone size-full wp-image-36525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-71.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 71\" width=\"10\" height=\"16\" \/> represent addition and multiplication (not necessarily in that order). Determine which symbol represents which operation. Justify your answer. Then state each algebraic property being illustrated.<\/p>\n<p><strong>LOOKING FOR STRUCTURE<\/strong><br \/>\nTo be proficient in math, you need to look closely to discern a pattern or structure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-72.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 72\" width=\"556\" height=\"291\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-72.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-72-300x157.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can algebraic properties help you solve an equation?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nSolve 3(x + 1) &#8211; 1 = &#8211; 13. Justify each step.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_2.4_Algebraic_Reasoning\"><\/a>Lesson 2.4 Algebraic Reasoning<\/h3>\n<p>Monitoring Progress<\/p>\n<p>Solve the equation. Justify each step.<\/p>\n<p>Question 1.<br \/>\n6x &#8211; 11 = &#8211; 35<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n&#8211; 2p &#8211; 9 = 10p &#8211; 17<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n39 &#8211; 5z = -1 + 5z<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n3(3x + 14) = &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n4 = &#8211; 10b + 6(2 &#8211; b)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nSolve the formula A = \\(\\frac{1}{2}\\)bh for b. Justify each step. Then find the base of a<br \/>\ntriangle whose area is 952 square feet and whose height is 56 feet.<br \/>\nAnswer:<\/p>\n<p>Name the property of equality that the statement illustrates.<\/p>\n<p>Question 7.<br \/>\nIf m\u22206 = m\u22207, then m\u22207 = m\u22206.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n34\u00b0 = 34\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nm\u22201 = m\u22202 and m\u22202 = m\u22205. So, m\u22201 = m\u22205.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nIf JK = KL and KL = 16, then JK = 16.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nPQ = ST, so ST = PQ.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nZY = ZY<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nIn Example 5. a hot dog stand is located halfway between the shoe store and the pizza shop. at point H. Show that PH = HM.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_2.4_Algebraic_Reasoning\"><\/a>Exercise 2.4 Algebraic Reasoning<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nThe statement \u201cThe measure of an angle is equal to itself\u201d is true because of what property?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 1\" width=\"297\" height=\"33\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find both answers.<br \/>\nWhat property justifies the following statement?<br \/>\nIf c = d, then d = c.<br \/>\nIf JK = LW. then LM = JK.<br \/>\nIf e = f and f = g, then e = g.<br \/>\nIf m\u2220R = m\u2220S, then m\u2220S = m\u2220R.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4, write the property that justifies each step.<\/p>\n<p>Question 3.<br \/>\n3x &#8211; 12 = 7x + 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Given<br \/>\n&#8211; 4x &#8211; 12 = 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0___________<br \/>\n&#8211; 4x = 20\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ___________<br \/>\nx = &#8211; 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ___________<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 3\" width=\"313\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-3.png 313w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-3-300x97.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/p>\n<p>Question 4.<br \/>\n5(x &#8211; 1) = 4x + 13\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Given<br \/>\n5x &#8211; 5 = 4x + 13\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ___________<br \/>\nx &#8211; 5 = 13\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ___________<br \/>\nx = 18\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0___________<br \/>\nAnswer:<\/p>\n<p>In Exercises 5 &#8211; 14. solve the equation. Justify each step.<\/p>\n<p>Question 5.<br \/>\n5x &#8211; 10 = &#8211; 40<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 5\" width=\"587\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-5.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-5-300x98.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 6.<br \/>\n6x + 17 = &#8211; 7<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n2x &#8211; 8 = 6x &#8211; 20<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 7\" width=\"556\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-7.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-7-300x137.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 8.<br \/>\n4x + 9 = 16 &#8211; 3x<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n5(3x &#8211; 20) = &#8211; 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 9\" width=\"546\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-9.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-9-300x123.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 10.<br \/>\n3(2x + 11) = 9<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n2(- x &#8211; 5) = 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 11\" width=\"551\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-11.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-11-300x123.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 12.<br \/>\n44 &#8211; 2(3x + 4) = &#8211; 18x<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n4(5x &#8211; 9) = &#8211; 2(x + 7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 13\" width=\"590\" height=\"316\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-13.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-13-300x161.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 14.<br \/>\n3(4x + 7) = 5(3x + 3)<br \/>\nAnswer:<\/p>\n<p>In Exercises 15 &#8211; 20, solve the equation for y. Justify each step.<\/p>\n<p>Question 15.<br \/>\n5x + y = 18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 15\" width=\"572\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-15.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-15-300x68.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 16.<br \/>\n&#8211; 4x + 2y = 8<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n2y &#8211; 0.5x = 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 17\" width=\"572\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-17.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-17-300x99.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{1}{2} x-\\frac{3}{4} y\\) = &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n12 &#8211; 3y = 30x + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 19\" width=\"578\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-19.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-19-300x98.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 20.<br \/>\n3x + 7 = &#8211; 7 + 9y<br \/>\nAnswer:<\/p>\n<p>In Exercises 21 &#8211; 24. solve the equation for the given variable. Justify each step<\/p>\n<p>Question 21.<br \/>\nC = 2\u03c0r; r<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 21\" width=\"580\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-21.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-21-300x104.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 22.<br \/>\nI = Prt;P<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nS = 180(n &#8211; 2); n<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 23\" width=\"592\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-23.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-23-300x140.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 24.<br \/>\n5 = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh; h<br \/>\nAnswer:<\/p>\n<p>In Exercises 25 &#8211; 32, name the property of equality that the statement illustrates.<\/p>\n<p>Question 25.<br \/>\nIf x = y, then 3x = 3y.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 25\" width=\"526\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-25.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-25-300x34.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 26.<br \/>\nIf AM = MB. then AM + 5 = MB + 5.<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nx = x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 27\" width=\"563\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-27.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-27-300x19.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 28.<br \/>\nIf x = y, then y = x.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nm\u2220Z = m\u2220Z<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 29\" width=\"561\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-29.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-29-300x18.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 30.<br \/>\nIf m\u2220Z = 29\u00b0 and m\u2220B = 29\u00b0, then m\u2220A = m\u2220B<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nIf AB = LM, then LM = AB.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 31\" width=\"563\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-31.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-31-300x17.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 32.<br \/>\nIf BC = XY and XY = 8, then BC = 8.<br \/>\nAnswer:<\/p>\n<p>In Exercises 33 &#8211; 40. use the property to copy and complete the statement.<\/p>\n<p>Question 33.<br \/>\nSubstitution Property of Equality:<br \/>\nIf AB = 20. then AB + CD = ________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 33\" width=\"378\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-33.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-33-300x27.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 34.<br \/>\nSymmetric Property o\u00cc Equality:<br \/>\nIf m\u22201 = m\u22202. then ________ .<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nAddition Property of Equality:<br \/>\nIf AB = CD. then AB + EF = ________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 35\" width=\"383\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-35.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-35-300x24.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Question 36.<br \/>\nMultiplication Property of Equality:<br \/>\nIf AB = CD, then 5 \u2022 AB = ________ .<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nSubtraction Property of Equality:<br \/>\nIf LM = XY, then LM &#8211; GH = ________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-37.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 37\" width=\"400\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-37.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-37-300x25.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 38.<br \/>\nDistributive Property:<br \/>\nIf 5(x + 8) = 2, then ___ + ___ = 2.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nTransitive Property of Equality:<br \/>\nIf m\u22201 = m\u22202 and m\u22202 = m\u22203, then ________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-39.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 39\" width=\"493\" height=\"29\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-39.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-39-300x18.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/p>\n<p>Question 40.<br \/>\nReflexive Properly of Equality:<br \/>\nm\u2220ABC = ________ .<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 41 and 42, describe and correct the error in solving the equation.<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-73.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 73\" width=\"324\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-73.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-73-300x123.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-41.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 41\" width=\"545\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-41.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-41-300x106.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-74.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 74\" width=\"335\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-74.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-74-300x114.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nThe formula for the perimeter P of a rectangle is P = 2l + 2w, where l is the length and w is the width. Solve the formula for l. Justify each step. Then find the length of a rectangular lawn with a perimeter of 32 meters and a width of 5 meters.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-43.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 43\" width=\"569\" height=\"405\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-43.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-43-300x214.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nThe formula for the area<br \/>\nA of a trapezoid is A = \\(\\frac{1}{2}\\)h (b<sub>1<\/sub> + b<sub>2<\/sub>), where h is the<br \/>\nheight and b<sub>1<\/sub> and b<sub>2<\/sub> are the lengths of the two bases. Solve the formula for b<sub>1<\/sub>. Justify each step. Then find the length of one of the bases of the trapezoid when the area of the trapezoid is 91 square meters. the height is 7 meters. and the length of the other base is 20 meters.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nIn the diagram,<br \/>\nm\u2220ABD = m\u2220CBE. Show that m\u22201 = m\u22203.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36521\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-75.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 75\" width=\"116\" height=\"143\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-45.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 45\" width=\"585\" height=\"425\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-45.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-45-300x218.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nIn the diagram,<br \/>\nAC = BD. Show that AB = CD.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-76.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 76\" width=\"275\" height=\"33\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nCopy and complete the table to show that m\u22202 = m\u22203.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"288\">Equation<\/td>\n<td style=\"text-align: center;\" width=\"210\">Reason<\/td>\n<\/tr>\n<tr>\n<td width=\"288\">m\u22201 = m\u22204, m\u2220EFH = 90\u00b0, m\u2220GHF = 90\u00b0<\/td>\n<td width=\"210\">Given<\/td>\n<\/tr>\n<tr>\n<td width=\"288\">m\u2220EHF = m\u2220GHF<\/td>\n<td width=\"210\"><\/td>\n<\/tr>\n<tr>\n<td width=\"288\">m\u2220EHF = m\u22201 + m\u22202<br \/>\nm\u2220GHF = m\u22203 + m\u22204<\/td>\n<td width=\"210\"><\/td>\n<\/tr>\n<tr>\n<td width=\"288\">m\u22201 + m\u22202 = m\u22203 + m\u22204<\/td>\n<td width=\"210\"><\/td>\n<\/tr>\n<tr>\n<td width=\"288\"><\/td>\n<td width=\"210\">Substitution Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"288\">m\u22202 = m\u22203<\/td>\n<td width=\"210\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-47.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 47\" width=\"572\" height=\"479\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-47.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-47-300x251.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the Reflexive Property of Equality with the Symmetric Property of Equality. How are the properties similar? How are they different?<br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong><br \/>\nIn Exercises 49 and 50. show that the perimeter of \u2206ABC is equal to the perimeter of \u2206ADC.<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36518\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-78.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 78\" width=\"151\" height=\"93\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-49.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 49\" width=\"577\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-49.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-49-300x188.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36517\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-79.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 79\" width=\"187\" height=\"93\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nIn the figure, \\(\\overline{Z Y}\\) \u2245 \\(\\overline{X W}\\), ZX = 5x + 17, YW = 10 &#8211; 2x, and YX = 3. Find ZY and XW<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36516\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-80.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 80\" width=\"191\" height=\"79\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-51.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 51\" width=\"553\" height=\"574\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-51.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-51-289x300.png 289w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe bar graph shows the number of hours each employee works at a grocery store. Give an example of the Reflexive, Symmetric, and Transitive Properties of Equality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36515\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-81.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 81\" width=\"261\" height=\"202\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nWhich of the following statements illustrate the Symmetric Property of Equality? Select all that apply.<br \/>\n(A) If AC = RS, then RS = AC.<br \/>\n<span style=\"font-size: 16px;\">(B) If x = 9 then 9 = x.<br \/>\n<\/span><span style=\"font-size: 16px;\">(C) If AD = BC, then DA = CB.<br \/>\n<\/span><span style=\"font-size: 16px;\">(D) AB = BA<br \/>\n<\/span><span style=\"font-size: 16px;\">(E) If AB = LW and LM = RT, then AB = RT.<br \/>\n<\/span><span style=\"font-size: 16px;\">(F) If XY = EF, then FE = XY.<br \/>\n<\/span><span style=\"font-size: 16px;\">Answer:<\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-53.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 53\" width=\"555\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-53.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-53-300x18.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite examples from your everyday life lo help you remember the Reflexive, Symmetric, and Transitive Properties of Equality. Justify your answers.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nThe formula to convert<br \/>\na temperature in degrees Fahrenheit (\u00b0F) to degrees<br \/>\nCelsius (\u00b0C) is C = \\(\\frac{5}{9}\\)(F &#8211; 32).<br \/>\na. Solve the formula for F. Justify each step.<br \/>\n<span style=\"font-size: 16px;\">b. Make a table that shows the conversion to Fahrenheit for each temperature: 0\u00b0C. 20\u00b0C, 32\u00b0C. and 41\u00b0C.<br \/>\n<\/span><span style=\"font-size: 16px;\">c. Use your table to graph the temperature in degrees Fahrenheit as a function of the temperature in degrees Celsius. Is this a linear function?<br \/>\n<\/span><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 55.1\" width=\"600\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.1.png 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.1-300x134.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 55.2\" width=\"609\" height=\"451\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.2.png 609w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.2-300x222.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 55.3\" width=\"612\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.3.png 612w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-55.3-300x161.png 300w\" sizes=\"(max-width: 612px) 100vw, 612px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>REASONING<\/strong><br \/>\nSelect all the properties that would also apply to inequalities. Explain your reasoning.<br \/>\n(A) Addition Property<br \/>\nAnswer:<\/p>\n<p>(B) Subtraction Properly<br \/>\nAnswer:<\/p>\n<p>(C) Substitution Property<br \/>\nAnswer:<\/p>\n<p>(D) Reflexive Property<br \/>\nAnswer:<\/p>\n<p>(E) Symmetric Property<br \/>\nAnswer:<\/p>\n<p>(F) Transitive Property<br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Name the definition property, or postulate that is represented by each diagram.<\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36514\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-82.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 82\" width=\"29\" height=\"153\" \/><br \/>\nXY + YZ = XZ<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-57.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 57\" width=\"351\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-57.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-57-300x30.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/p>\n<p>Question 58.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36513\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-83.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 83\" width=\"125\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-84.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 84\" width=\"31\" height=\"146\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.4-Question-59.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.4 Question 59\" width=\"104\" height=\"32\" \/><\/p>\n<p>Question 60.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Solutions-Chapter-2-Reasoning-and-Proofs-85.png\" alt=\"Big Ideas Math Geometry Solutions Chapter 2 Reasoning and Proofs 85\" width=\"138\" height=\"131\" \/><br \/>\nm\u2220ABD + m\u2220DBC = m\u2220ABC<br \/>\nAnswer:<\/p>\n<h3><a id=\"2.5_Proving_Statements_about_Segments_and_Angles\"><\/a>2.5 Proving Statements about Segments and Angles<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing Reasons in a proof<\/p>\n<p>Work with a partner: Four steps of a proof are shown. Write the reasons for each statement<br \/>\nGiven AC = AB + AB<br \/>\nProve AB = BC<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-86.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 86\" width=\"197\" height=\"33\" \/><\/p>\n<p><strong>REASONING ABSTRACTLY<\/strong><br \/>\nTo be proficient in math, you need to know and be able to use algebraic properties.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"144\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"198\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"144\">1. AC = AB + AB<\/td>\n<td width=\"198\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"144\">2. AB = BC\u00a0 = AC<\/td>\n<td width=\"198\">2. ______________________<\/td>\n<\/tr>\n<tr>\n<td width=\"144\">3. AB + AB = AB + BC<\/td>\n<td width=\"198\">3. ______________________<\/td>\n<\/tr>\n<tr>\n<td width=\"144\">4. AB = BC<\/td>\n<td width=\"198\">4. ______________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Writing Steps in a Proof<\/p>\n<p>Work with a partner: Six steps of a proof are shown. Complete the statements that correspond to each reason.<br \/>\nGiven m\u22201 = m\u22203<br \/>\nProve m\u2220EBA = m\u2220CBD<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-87.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 87\" width=\"153\" height=\"112\" \/><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. ___________________________<\/td>\n<td width=\"312\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. m\u2220EBA = m\u22202 + m\u22203<\/td>\n<td width=\"312\">2. Angle Addition Postulate (Post.1.4)<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. m\u2220EBA = m\u22202 + m\u22201<\/td>\n<td width=\"312\">3. Substitution Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. m\u2220EBA = ___________________________<\/td>\n<td width=\"312\">4. Commutative Property of Addition<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">5. m\u22201 + m\u22202 = ______________________<\/td>\n<td width=\"312\">5. Angle Addition Postulate (Post. 1.4)<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">6. ________________________________________<\/td>\n<td width=\"312\">6. Transitive Property of Equality<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you prove a mathematical statement?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse the given information and the figure to write a proof for the statement.<br \/>\nGiven B is the midpoint of \\(\\overline{A C}\\).<br \/>\nC is the midpoint of \\(\\overline{B D}\\).<br \/>\nProve AB = CD<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-88.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 88\" width=\"235\" height=\"37\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_2.5_Proving_Statements_about_Segments_and_Angles\"><\/a>Lesson 2.5 Proving Statements about Segments and Angles<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nSix Steps of a two-column proof are shown. Copy and complete the proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-89.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 89\" width=\"291\" height=\"34\" \/><br \/>\nGiven T is the midpoint of \\(\\overline{S U}\\).<br \/>\nProve x = 5<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statement<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reason<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. T is the midpoint of \\(\\overline{S U}\\).<\/td>\n<td width=\"312\">1. ________________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. \\( \\overline{S T} \\cong \\overline{T U} \\)<\/td>\n<td width=\"312\">2. Definition of midpoint<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. ST = TU<\/td>\n<td width=\"312\">3. Definition of congruent segments<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. 7x = 3x + 20<\/td>\n<td width=\"312\">4. ________________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">5. ________________________________________<\/td>\n<td width=\"312\">5. Subtraction Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">6. x = 5<\/td>\n<td width=\"312\">6. ________________________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<h3><a id=\"Exercise_2.5_Proving_Statements_about_Segments_and_Angles\"><\/a>Exercise 2.5 Proving Statements about Segments and Angles<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b><br \/>\nHow is a theorem different from a postulate?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 1\" width=\"567\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-1.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-1-300x45.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nIn a two-column proof, each __________ is on the left and each __________ is on the right.<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3 and 4. copy and complete the proof.<\/p>\n<p>Question 3.<br \/>\nGiven PQ = RS<br \/>\nProve PR = QS<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-90.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 90\" width=\"191\" height=\"39\" \/><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. PQ = RS<\/td>\n<td width=\"312\">1. ________________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. PQ + QR = RS + QR<\/td>\n<td width=\"312\">2. ________________________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. ________________________________________<\/td>\n<td width=\"312\">3. Segment Addition Postulate (Post. 1.2)<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. RS + QR = QS<\/td>\n<td width=\"312\">4. Segment Addition Postulate (Post. 1.2)<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">5. PR = QS<\/td>\n<td width=\"312\">5. ________________________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 3\" width=\"539\" height=\"462\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-3.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-3-300x257.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 4.<br \/>\nGiven \u22201 is a complement of \u22202.<br \/>\n\u22202 \u2245 \u22203<br \/>\nProve \u22201 is a complement of \u22203.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-91.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 91\" width=\"197\" height=\"92\" \/><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. \u22201 is a complement of \u22202.<\/td>\n<td width=\"312\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. \u22202 \u2245 \u22203<\/td>\n<td width=\"312\">2. _____________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. m\u22201 + m\u22202 = 90\u00b0<\/td>\n<td width=\"312\">3. _____________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. m\u22202 = m\u22203<\/td>\n<td width=\"312\">4.\u00a0 Definition of congruent angles<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">5. _____________________________<\/td>\n<td width=\"312\">5. Substitution Property Of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">6. \u22201 is a complement of \u22203.<\/td>\n<td width=\"312\">6. _____________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p>In Exercises 5-10, name the property that the statement illustrates.<\/p>\n<p>Question 5.<br \/>\nIf \\(\\overline{P Q} \\cong \\overline{S T}\\) and \\(\\overline{S T} \\cong \\overline{U V}\\), then \\(\\overline{P Q} \\cong \\overline{U V}\\).\\<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 5\" width=\"510\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-5.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-5-300x21.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 6.<br \/>\n\u2220F \u2245 \u2220F<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nIf \u2220G \u2245\u2220H. then \u2220H \u2245 \u2220G.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 7\" width=\"496\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-7.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-7-300x19.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\overline{D E} \\cong \\overline{D E}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nIf \\(\\overline{X Y} \\cong \\overline{U V}\\), then \\(\\overline{U V} \\cong \\overline{X Y}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 9\" width=\"519\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-9.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-9-300x21.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 10.<br \/>\nIf \u2220L \u2245\u2220M and \u2220M \u2245\u2220N, then \u2220L \u2245\u2220N.<br \/>\nAnswer:<\/p>\n<p>PROOF<br \/>\nIn Exercises 11 and 12, write a two-column proof for the property.<\/p>\n<p>Question 11.<br \/>\nReflexive Property of Segment Congruence (Thm. 2.1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 11\" width=\"572\" height=\"426\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-11.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-11-300x223.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 12.<br \/>\nTransitive Property of Angle Congruence (Thm. 2.2)<br \/>\nAnswer:<\/p>\n<p><strong>PROOF<\/strong><br \/>\nExercises 13 and 14. write a two-column proof.<\/p>\n<p>Question 13.<br \/>\nGiven \u2220GFH \u2245 \u2220GHF<br \/>\nProve \u2220EFG and \u2220GHF are supplementary<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-92.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 92\" width=\"191\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 13\" width=\"559\" height=\"647\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-13.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-13-259x300.png 259w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-93.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 93\" width=\"213\" height=\"75\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-94.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 94\" width=\"77\" height=\"183\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nIn the diagram \\(\\overline{M N} \\cong \\overline{L Q}\\) and \\(\\overrightarrow{L Q} \\cong \\overrightarrow{P N}\\). Describe and correct the error in the reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-95.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 95\" width=\"358\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-95.png 358w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-95-300x103.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 15\" width=\"566\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-15.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-15-300x59.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 16.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe distance fr the restaurant to the shoe store is the same as the distance from the cafe to the florist. The distance from the shoe store to the movie theater is the same as the distance from the movie theater to the cafe, and from the florist to the dry cleaners.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-96.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 96\" width=\"359\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-96.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-96-300x107.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><br \/>\nUse the steps below to prove that the distance from the restaurant to the movie theater is the same as the distance from the cafe to the dry cleaners.<br \/>\na. State what is given and what is to be proven for the situation.<br \/>\nAnswer:<\/p>\n<p>b. Write a two-column proof.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn the sculpture shown, \\(\\angle 1 \\cong \\angle 2\\) and \\(\\angle 2 \\cong \\angle 3\\) classify the triangle and justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-97.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 97\" width=\"138\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-17.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 17\" width=\"569\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-17.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-17-300x75.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nIn the figure, \\(\\overline{S R} \\cong \\overline{C B}\\) and \\(\\overline{A C} \\cong \\overline{Q R}\\) Your friend claims that, because of this. \\( \\overline{C B} \\cong \\overline{A C}\\) by the Transitive Property of Segment Congruence (Thin. 2. 1). Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-98.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 98\" width=\"160\" height=\"65\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why you do not use inductive reasoning when writing a proof.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-19.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 19\" width=\"579\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-19.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-19-300x102.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the figure to write Given and Prove statements for each conclusion.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-99.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 99\" width=\"194\" height=\"97\" \/><br \/>\na. The acute angles of a right triangle are complementary.<br \/>\nb. A segment connecting the midpoints of two sides of a triangle is half as long as the third side.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nFold two corners of a piece of paper So their edges match. as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-100.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 100\" width=\"163\" height=\"198\" \/><br \/>\na. What do you notice about the angle formed at the top of the page by the folds?<br \/>\n<span style=\"font-size: 16px;\">b. Write a two-column proof to show that the angle measure is always the same no matter how you make the folds.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 21\" width=\"564\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-21.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-21-300x135.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/span><\/p>\n<p>Question 22.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe distance from Springfield<br \/>\nto Lakewood City is equal to the distance from Springfield Lo BettsilIe. Janisburg is 50 miles farther from Springfield titan Bettsville. Moon Valley is 50 miles Farther from Springfield than Lakewood City is. Use line segments to draw a diagram that represents this situation.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nSolve for x using the given information. Justify each step.<br \/>\nGiven \\(\\overline{Q R} \\cong \\overline{P Q}, \\overline{R S} \\cong \\overline{P Q}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-101.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 101\" width=\"200\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-23.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 23\" width=\"559\" height=\"627\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-23.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-23-267x300.png 267w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Use the figure<\/p>\n<p>Question 24.<br \/>\n\u2220 1 is a complement of \u22204. and m\u22201 33\u00b0. Find in m\u22204.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n\u22203 is a supplement of \u22202, and m\u22202 = 147\u00b0. Find m\u22203.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.5-Question-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.5 Question 25\" width=\"282\" height=\"132\" \/><\/p>\n<p>Question 26.<br \/>\nName a pair of vertical angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Geometry-Chapter-2-Reasoning-and-Proofs-102.png\" alt=\"Big Ideas Math Answer Key Geometry Chapter 2 Reasoning and Proofs 102\" width=\"180\" height=\"86\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"2.6_Proving_Geometric_Relationships\"><\/a>2.6 Proving Geometric Relationships<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Matching Reasons in a Flowchart Proof<\/p>\n<p>work with a partner: Match each reason with the correct step in the flowchart.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-103.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 103\" width=\"196\" height=\"34\" \/><br \/>\nGiven AC = AB + AB<br \/>\nProve AB = BC<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-104.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 104\" width=\"555\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-104.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-104-300x90.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p><strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nTo be proficient in math, you need to map relationships using such tools as diagrams, two-way tables, graphs, flowcharts, and formulas.<\/p>\n<p>A. Segment Addition Postulate (Post. 1.2)<br \/>\nAnswer:<\/p>\n<p>B. Given<br \/>\nAnswer:<\/p>\n<p>C. Transitive Property of Equality<br \/>\nAnswer:<\/p>\n<p>D. Subtraction Property of Equality<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Matching Reasons in a Flowchart Proof<\/p>\n<p>Work with a partner. Match each reason with the Correct step in the flowchart.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-105.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 105\" width=\"147\" height=\"114\" \/><br \/>\nGiven m\u22201 = m\u22203<br \/>\nProve m\u2220EBA = m\u2220CBD<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-106.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 106\" width=\"679\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-106.png 679w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-106-300x108.png 300w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><br \/>\nA. Angle Addition Postulate (Post. 1.4)<br \/>\nAnswer:<\/p>\n<p>B. Transitive Property of Equality<br \/>\nAnswer:<\/p>\n<p>C. Substitution Property of Equality<br \/>\nAnswer:<\/p>\n<p>D. Angle Addition Postulate (Post. 1.4)<br \/>\nAnswer:<\/p>\n<p>E. Given<br \/>\nAnswer:<\/p>\n<p>F. Commutative Property of Addition<br \/>\nAnswer:<\/p>\n<p>Communicate Your Answer<\/p>\n<p>Question 3.<br \/>\nHow can you use a flowchart to prove a mathematical statement?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nCompare the flowchart proofs above with the two-column proofs in the Section 2.5 Explorations. Explain the advantages and disadvantages of each.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lessson_2.6_Proving_Geometric_Relationships\"><\/a>Lessson 2.6 Proving Geometric Relationships<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nCopy and complete the flowchart proof. Then write a two-column proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-107.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 107\" width=\"182\" height=\"82\" \/><br \/>\nGiven \\(\\overline{A B}\\) \u22a5 \\(\\overline{B C}\\), \\(\\overline{D C}\\) \u22a5 \\(\\overline{B C}\\)<br \/>\nProve \u2220B \u2245\u2220C<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-108.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 108\" width=\"488\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-108.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-108-300x46.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nCopy and complete the two-column proof. Then write a flowchart proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-109.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 109\" width=\"257\" height=\"31\" \/><br \/>\nGiven AB = DE, BC = CD<br \/>\nProve \\(\\overline{A C} \\cong \\overline{C E}\\)<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. AB = DE, BC = CD<\/td>\n<td width=\"312\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. AB + BC = BC + DE<\/td>\n<td width=\"312\">2. Addition Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. _____________________________<\/td>\n<td width=\"312\">3. Substitution Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. AB + BC = AC, CD + DE = CE<\/td>\n<td width=\"312\">4. _____________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">5. _____________________________<\/td>\n<td width=\"312\">5. Substitution Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">6. \\( \\overline{A C} \\cong \\overline{C E} \\)<\/td>\n<td width=\"312\">6. _____________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p>Question 3.<br \/>\nRewrite the two-column proof in Example 3 without using the Congruent Supplements Theorem. How many steps do you save by using the theorem?<br \/>\nAnswer:<\/p>\n<p>Use the diagram and the given angle measure to find the other three angle measures.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-110.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 110\" width=\"166\" height=\"104\" \/><\/p>\n<p>Question 4.<br \/>\nm\u22201 = 117\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nm\u22202 = 59\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nm\u22204 = 88\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nFind the value of w.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-111.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 111\" width=\"142\" height=\"123\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nwrite a paragraph proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-112.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 112\" width=\"190\" height=\"84\" \/><br \/>\nGiven \u22201 is a right angle.<br \/>\nProve \u22202 is a right angle.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exercise_2.6_Proving_Geometric_Relationships\"><\/a>Exercise 2.6 Proving Geometric Relationships<\/h3>\n<p>Vocabulary and Core Concept Check<\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why all right angles are congruent.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 1\" width=\"547\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-1.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-1-300x32.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat are the two types of angles that are formed by intersecting lines?<br \/>\nAnswer:<\/p>\n<p>Monitoring Progress and Modeling with Mathematics<\/p>\n<p>In Exercises 3-6. identify the pairs) of congruent angles in the figures. Explain how you know they are congruent.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-113.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 113\" width=\"167\" height=\"98\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-3.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 3\" width=\"583\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-3.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-3-300x114.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-114.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 114\" width=\"269\" height=\"85\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-115.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 115\" width=\"247\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-5.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 5\" width=\"588\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-5.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-5-300x86.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 6.<br \/>\n\u2220ABC is supplementary to \u2220CBD<br \/>\n\u2220CBD is supplementary to \u2220DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-116.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 116\" width=\"238\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 7 &#8211; 10. use the diagram and the given angle measure to find the other three measures.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-117.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 117\" width=\"213\" height=\"119\" \/><\/p>\n<p>Question 7.<br \/>\nm\u22201 = 143\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-7.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 7\" width=\"442\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-7.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-7-300x205.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>Question 8.<br \/>\nm\u22203 = 159\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nm\u22202 = 34\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-9.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 9\" width=\"443\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-9.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-9-300x205.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Question 10.<br \/>\nm\u22204 = 29\u00b0<br \/>\nAnswer:<\/p>\n<p>In Exercises 11 &#8211; 14, find the values of x and y.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-118.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 118\" width=\"136\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-11.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 11\" width=\"571\" height=\"380\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-11.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-11-300x200.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-119.png\" alt=\"\" width=\"170\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-120.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 120\" width=\"164\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-13.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 13\" width=\"597\" height=\"507\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-13.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-13-300x255.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-121.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 121\" width=\"185\" height=\"80\" \/><br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\nIn Exercises 15 and 16, describe and correct the error in using the diagram to find the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-122.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 122\" width=\"194\" height=\"93\" \/><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-123.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 123\" width=\"323\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-123.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-123-300x113.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-15.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 15\" width=\"528\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-15.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-15-300x112.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-124.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 124\" width=\"318\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-124.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-124-300x115.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nPROOF<br \/>\nCopy and complete the flowchart proof. Then write a two-column proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-125.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 125\" width=\"154\" height=\"100\" \/><br \/>\nGiven \u22201 \u2245 \u22203<br \/>\nProve \u22202 \u2245 \u22204<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-126.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 126\" width=\"602\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-126.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-126-300x48.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-17.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 17.1\" width=\"603\" height=\"457\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-17.1.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-17.1-300x227.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-17.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 17.2\" width=\"594\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-17.2.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-17.2-300x132.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>PROOF<\/strong><br \/>\nCopy and complete the two-column proof. Then write a flowchart proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-127.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 127\" width=\"101\" height=\"179\" \/><br \/>\nGiven \u2220ABD is a right angle<br \/>\n\u2220CBE is a right angle<br \/>\nProve \u2220ABC \u2245 \u2220DBE<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. \u2220ABD is a right angle.<\/p>\n<p>\u2220CBE is a right angle.<\/td>\n<td width=\"312\">1. _____________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. \u2220ABC and \u2220CBD are complementary.<\/td>\n<td width=\"312\">2. Definition of complementary<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. \u2220DBE and \u2220CBD are complementary<\/td>\n<td width=\"312\">3. _____________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. \u2220ABE \u2245 \u2220DBE<\/td>\n<td width=\"312\">4. _____________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Question 19.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nCopy and complete the paragraph proof be the Congruent Complements Theorem (Theorem 2.5). Then write a two-column proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-128.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 128\" width=\"149\" height=\"91\" \/><br \/>\nGiven \u22201 and \u22202 are complementary<br \/>\n\u22201 and \u22203 are complementary<br \/>\nProve \u22202 \u2245 \u22203<br \/>\n\u22201 and \u22202 are complementary, and \u22201 and \u22203 are complementary. By the definition<br \/>\nof ____________ angles. m\u22201 + m\u22202 = 90\u00b0 and ____________ = 90\u00b0. By the ____________ m\u22201 + m\u22202 = m\u22201 + m\u22203. By the Subtraction ____________<br \/>\nProperty of Equality, ____________ . So. \u22202 \u2245\u22203 by the definition of ____________ .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-19.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 19.1\" width=\"663\" height=\"389\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-19.1.png 663w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-19.1-300x176.png 300w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-19.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 19.2\" width=\"658\" height=\"394\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-19.2.png 658w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-19.2-300x180.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>PROVING A THEOREM<\/strong><br \/>\nCopy and complete the two &#8211; column proof for the Congruent Supplement Theorem (Theorem 2.4). Then write a paragraph proof. (See Example 5.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-129.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 129\" width=\"232\" height=\"77\" \/><br \/>\nGiven \u22201 and \u22202 are supplementary<br \/>\n\u22203 and \u22204 are supplementary<br \/>\n\u22201 and \u22204<br \/>\nProve \u22202 \u2245\u22203<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. \u22201 and \u22202 are supplementary<br \/>\n\u22203 and \u22204 are supplementary<br \/>\n\u22201 \u2245 \u22204<\/td>\n<td width=\"312\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. m\u22201 + m\u22202 = 180<br \/>\nm\u22203 + m\u22204 = 180<\/td>\n<td width=\"312\">2. _____________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. ______________ = m\u22203 + m\u22204<\/td>\n<td width=\"312\">3. Transitive Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. m\u22201 = m\u22204<\/td>\n<td width=\"312\">4. Definition of Congruent angles<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">5. m\u22201 + m\u22202 = ___________________<\/td>\n<td width=\"312\">5. Substitution property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">6. m\u22202 = m\u22203<\/td>\n<td width=\"312\">6. _____________________________<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">7. __________________________<\/td>\n<td width=\"312\">7. _____________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p><strong>PROOF<\/strong><br \/>\nIn Exercises 21 &#8211; 24. write a proof using any format.<\/p>\n<p>Question 21.<br \/>\nGiven \u2220QRS and \u2220PSR are supplementary<br \/>\nProve \u2220QRL \u2245 \u2220PSR<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-130.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 130\" width=\"133\" height=\"209\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-21.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 21\" width=\"602\" height=\"582\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-21.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-21-300x290.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 22.<br \/>\nGiven \u22201 and \u22203 are complementary.<br \/>\n\u22202 and \u22204 are complementary.<br \/>\nProve \u22201 \u2245 \u22204<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-131.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 131\" width=\"267\" height=\"185\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nGiven \u2220AEB \u2245 \u2220DEC<br \/>\nProve \u2220AEC \u2245 \u2220DEB<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-132.png\" alt=\"\" width=\"154\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-23.1.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 23.1\" width=\"258\" height=\"238\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-23.2.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 23.2\" width=\"550\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-23.2.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-23.2-300x273.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-133.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 133\" width=\"218\" height=\"73\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-134.png\" alt=\"\" width=\"166\" height=\"74\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou overhear your friend discussing the diagram shown with a classmate. Your classmate claims \u22201 \u2245\u22204 because they are vertical angles Your friend claims they are not congruent because he can tell by looking at the diagram. Who is correct? Support your answer with definitions or theorems.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-135.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 135\" width=\"114\" height=\"86\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-25.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 25\" width=\"557\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-25.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-25-300x64.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nDraw three lines all intersecting at the same point. Explain how you can give two of the angle measures so that you can find the remaining four angle measures.<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs the converse of the Linear Pair Postulate (Postulate 2.8) true? If so, write a biconditional statement. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-27.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 27\" width=\"549\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-27.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-27-300x64.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow can you save time writing proofs?<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nFind the measure of each angle in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-136.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 136\" width=\"214\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-29.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 29\" width=\"335\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-29.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-29-217x300.png 217w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the student\u2019s two-column proof.<br \/>\nGiven \u22201 \u2245 \u22202<br \/>\n\u22201 and \u22202 are supplementary.<br \/>\nProve ___________<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. \u22201 \u2245 \u22202<br \/>\n\u22201 and \u22202 are supplementary<\/td>\n<td width=\"312\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. m\u22201 = m\u22202<\/td>\n<td width=\"312\">2. Definitions of congruent angles<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. m\u22201 + m\u22202 = 180\u00b0<\/td>\n<td width=\"312\">3. Definition of supplementary angles<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. m\u22201 + m\u22201 = 180\u00b0<\/td>\n<td width=\"312\">4. substitution property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">5. 2m\u22201 = 180\u00b0<\/td>\n<td width=\"312\">5. Simplify<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">6. m\u22201 = 90\u00b0<\/td>\n<td width=\"312\">6. Division Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">7. m\u22202 = 90\u00b0<\/td>\n<td width=\"312\">7. Transitive Property of Equality<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">8. __________________________<\/td>\n<td width=\"312\">8. ________________________________________<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>a What is the student trying to prove?<br \/>\nAnswer:<\/p>\n<p>b. Your friend claims that the last line of the proof should be \u22201 \u2245 \u22202. because the measures of the angles are both 90\u00b0. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Maintaining Mathematical Proficiency<\/p>\n<p>Use the cube<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-137.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 137\" width=\"217\" height=\"208\" \/><\/p>\n<p>Question 31.<br \/>\nName three collinear points.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-31.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 31\" width=\"406\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-31.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-31-300x24.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 32.<br \/>\nName the intersection of plane ABF and plane EHG.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nName two planes containing \\(\\overline{B C}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-33.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 33\" width=\"537\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-33.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-33-300x53.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 34.<br \/>\nName three planes containing point D.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nName three points that are not collinear,<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-35.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 2.6 Question 35\" width=\"572\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-35.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-2.6-Question-35-300x29.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 36.<br \/>\nName two planes containing point J.<br \/>\nAnswer:<\/p>\n<h3><a id=\"2.4_-_2.6_Performance_Task:_Induction_and_the_Next_Dimension\"><\/a>2.4 &#8211; 2.6 Performance Task: Induction and the Next Dimension<\/h3>\n<p>Mathematical Practices<\/p>\n<p>Question 1.<br \/>\nExplain the purpose of justifying each step in Exercises 5-14 on page 96.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nCreate a diagram to model each statement in Exercises 5-10 on page 103.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nExplain why you would not be able to prove the statement in Exercise 21 on page 113 if you were provided with the given information or able to use an postulates or theorems.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Reasoning_and_Proofs_Chapter_Review\"><\/a>Reasoning and Proofs Chapter Review<\/h3>\n<h4>2.1 Conditional Statements<\/h4>\n<p>Write the if-then form, the converse, the inverse, the contrapositive. and the biconditional of the conditional statement.<\/p>\n<p>Question 1.<br \/>\nTwo lines intersect in a Point.<\/p>\n<p>Question 2.<br \/>\n4x + 9 = 21 because x = 3.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nSupplementary angles sum to 180\u00b0.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nRight angles are 90\u00b0.<br \/>\nAnswer:<\/p>\n<h4>2.2 Inductive and Deductive Reasoning<\/h4>\n<p>Question 5<br \/>\nconclusion can you make about the difference of any two odd integers?<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nWhat conclusion can you make about the product of an even and an odd integer?<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nUse the Law of Detachment to make a valid conclusion.<br \/>\nIf an angle is a right angle, then the angle measures 90\u00b0. \u2220B is a right angle.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nUse the Law of Syllogism to write a new conditional statement that follows from the pair of true statements: If x = 3, then 2x = 6. If 4x = 12. then x = 3.<br \/>\nAnswer:<\/p>\n<h4>2.3 Postulates and Diagrams<\/h4>\n<p>Use the diagram at the right to determine whether you can assume the statement.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-138.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 138\" width=\"261\" height=\"181\" \/><\/p>\n<p>Question 9.<br \/>\nPoints A, B, C, and E are coplanar.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-139.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 139\" width=\"82\" height=\"27\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nPoints F, B, and G are collinear.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-140.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 140\" width=\"75\" height=\"26\" \/><br \/>\nAnswer:<\/p>\n<p>sketch a diagram of the description.<\/p>\n<p>Question 13.<br \/>\n\u2220ABC, an acute angle, is bisected by <img loading=\"lazy\" class=\"alignnone size-full wp-image-36815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-141.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 141\" width=\"29\" height=\"26\" \/>.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n\u2220CDE, a straight angle, is bisected by <img loading=\"lazy\" class=\"alignnone size-full wp-image-36814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-142.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 142\" width=\"33\" height=\"25\" \/>.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nPlane P and plane R intersect perpendicularly in <img loading=\"lazy\" class=\"alignnone size-full wp-image-36813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Geometry-Answers-Chapter-2-Reasoning-and-Proofs-143.png\" alt=\"Big Ideas Math Geometry Answers Chapter 2 Reasoning and Proofs 143\" width=\"36\" height=\"27\" \/>. \\(\\overline{Z W}\\) lies in plane P<br \/>\nAnswer:<\/p>\n<h4>2.4 Algebraic Reasoning<\/h4>\n<p>Solve the equation. Justify each step.<\/p>\n<p>Question 16.<br \/>\n&#8211; 9x &#8211; 21 = &#8211; 20x &#8211; 87<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n15x + 22 = 7x + 62<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n3(2x + 9) = 30<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n5x + 2(2x &#8211; 23) = &#8211; 154<br \/>\nAnswer:<\/p>\n<p>Name the property of equality that the statement illustrates.<\/p>\n<p>Question 20.<br \/>\nIf LM = RS and RS = 25, then LM = 25.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nAM = AM<br \/>\nAnswer:<\/p>\n<h4>2.5 Proving Statements about Segments and Angles<\/h4>\n<p>Name the property that the statement illustrates.<\/p>\n<p>Question 22.<br \/>\nIf \u2220DEF \u2245\u2220JKL, then \u2220JKL \u2245 \u2220DEF<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n\u2220C \u2245 \u2220C<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nIf MN = PQ and PQ = RS. then MN = RS.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nWrite a two-column proof be the Reflexive Property of Angle Congruence (Thm. 2.2).<br \/>\nAnswer:<\/p>\n<h4>2.6 Proving Geometric Relationships<\/h4>\n<p>Question 26.<br \/>\nWrite a proof using any format<br \/>\nGiven \u22203 and \u22202 are complementary.<br \/>\nm\u22201 + m\u22202 = 90\u00b0<br \/>\nProve \u22203 \u2245\u22201<br \/>\nAnswer:<\/p>\n<h3><a id=\"Reasoning_and_Proofs_Test\"><\/a>Reasoning and Proofs Test<\/h3>\n<p>Use the diagram to determine whether you can assume the statement.<br \/>\nExplain your reasoning.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-144.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 144\" width=\"263\" height=\"185\" \/><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-145.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 145\" width=\"35\" height=\"25\" \/> \u22a5 plane M<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nPoints F, G, and A are coplanar.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nPoints E, C, and G are collinear.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nPlanes M and P intersect at <img loading=\"lazy\" class=\"alignnone size-full wp-image-36826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-146.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 146\" width=\"33\" height=\"25\" \/>.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-147.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 147\" width=\"31\" height=\"25\" \/> lies in plane P.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-148.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 148\" width=\"195\" height=\"30\" \/><br \/>\nAnswer:<\/p>\n<p>Solve the equation. Justify each step.<\/p>\n<p>Question 7.<br \/>\n9x + 31 = &#8211; 23 + 3x<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n26 + 2(3x + 11) = &#8211; 18<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n3(7x &#8211; 9) &#8211; 19x &#8211; 15<br \/>\nAnswer:<\/p>\n<p>Write the if-then form, the converse, the inverse, the contrapositive. and the biconditional of the conditional statement.<\/p>\n<p>Question 10.<br \/>\nTwo planes intersect at a line.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nA relation that pairs each input with exactly one output is a function.<br \/>\nAnswer:<\/p>\n<p>Use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to sIm that the conjecture is true.<\/p>\n<p>Question 12.<br \/>\nthe sum of three odd integers<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nthe product of three even integers<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nGive an example of two statements for which the Law of Detachment does not apply.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nThe formula for the area A of a triangle is A = \\(\\frac{1}{2}\\)bh, where b is the base and h is the height. Solve the formula for h and justify each step. Then find the height of a standard yield sign when the area is 558 square inches and each side is 36 inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-149.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 149\" width=\"166\" height=\"147\" \/><br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nYou visit the zoo and notice the following<\/p>\n<ul>\n<li>The elephants, giraffes, lions, tigers, and zebras are located along a straight walkway.<\/li>\n<li>The giraffes are halfway between the elephants and the lions.<\/li>\n<li>The tigers are halfway between the lions and the zebras.<\/li>\n<li>The lions are hallway between the giraffes and the tigers.<\/li>\n<\/ul>\n<p>Draw and label a diagram that represents this information. Then prove that the distance between the elephants and the giraffes is equal to the distance between the tigers and the zebras. Use any proof format.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nWrite a proof using an format.<br \/>\nGiven \u22202 \u2245\u22203<br \/>\n\\(\\vec{T}\\)V bisects \u2220UTW.<br \/>\nProve \u22201 \u2245 \u22203<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-150.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 150\" width=\"328\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-150.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-150-300x147.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Reasoning_and_Proofs_Cumulative_Assessment\"><\/a>Reasoning and Proofs Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nUse the diagram to write an example of each postulate.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-151.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 151\" width=\"216\" height=\"202\" \/><br \/>\na. Two Point Postulate (Postulate 2.1): Through any two points, there exists exactly one line.<br \/>\nAnswer:<\/p>\n<p>b. Line Intersection Postulate (Postulate 2.3): If two lines intersect, then their intersection is exactly one point.<br \/>\nAnswer:<\/p>\n<p>c. Three Point Postulate (Postulate 2.4): Through any three noncollinear points, there exists exactly one plane.<br \/>\nAnswer:<\/p>\n<p>d. Plane-Line Postulate (Postulate 2.6): If two points lie in a plane, then the line containing them lies in the plane.<br \/>\nAnswer:<\/p>\n<p>e. Plane Intersection Postulate (Postulate 2.7): If two planes intersect, then their intersection is a line<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nEnter the reasons in the correct positions to complete the two-column proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-152.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 152\" width=\"702\" height=\"374\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-152.png 702w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-152-300x160.png 300w\" sizes=\"(max-width: 702px) 100vw, 702px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nClassify each related conditional statement. based on the conditional statement<br \/>\n&#8220;If I study, then I will pass the final exam.&#8221;<br \/>\na. I will pass the final exam if and only if I study.<br \/>\nAnswer:<\/p>\n<p>b. If I do not study, then I will not pass the final exam.<br \/>\nAnswer:<\/p>\n<p>c. If I pass the final exam, then I studied.<br \/>\nAnswer:<\/p>\n<p>d. If I do not pass the final exam, then I did not study.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nList all segment bisectors given x = 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-153.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 153\" width=\"541\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-153.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-153-300x51.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nYou are given m\u2220FHE = m\u2220BHG = m\u2220AHF = 90\u00b0. Choose the symbol that makes each statement true. State which theorem or postulate. if any, supports your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-154.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 154\" width=\"218\" height=\"171\" \/><\/p>\n<p>=\u00a0 \u00a0 \u00a0 \u00a0\u2245\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2260<br \/>\na. \u22203 _____ \u22206<br \/>\nAnswer:<\/p>\n<p>b. m\u22204 ______ m\u22207<br \/>\nAnswer:<\/p>\n<p>c. m\u2220FHE _______ m\u2220AHG<br \/>\nAnswer:<\/p>\n<p>d. m\u2220AHG + m\u2220GHE _______180\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nFind the distance between each pair of points. Then order each line<br \/>\nsegment from longest to shortest.<br \/>\na. A(- 6, 1), B(- 1, 6)<br \/>\nAnswer:<\/p>\n<p>b. C(- 5, 8), D(5, 8)<br \/>\nAnswer:<\/p>\n<p>c. E(2, 7), F(4, &#8211; 2)<br \/>\nAnswer:<\/p>\n<p>d. G(7, 3), H(7, &#8211; 1)<br \/>\nAnswer:<\/p>\n<p>e. J(- 4, &#8211; 2), K(1, &#8211; 5)<br \/>\nAnswer:<\/p>\n<p>f. L(3, &#8211; 8), M(7, &#8211; 5)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nThe proof shows that \u2220MRL is congruent to \u2220NSR. Select all other angles that are also congruent to \u2220NSR.<br \/>\nGiven \u2220MRS and \u2220NSR are supplementary.<br \/>\nProve \u2220MRL \u2245 \u2220VSR<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-155.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 155\" width=\"207\" height=\"137\" \/><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"312\">Statements<\/td>\n<td style=\"text-align: center;\" width=\"312\">Reasons<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">1. \u2220MRS and \u2220NSR are supplementary<\/td>\n<td width=\"312\">1. Given<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">2. \u2220MRL and \u2220MRS are a linear pair.<\/td>\n<td width=\"312\">2. Definition of linear pair, as shown in the diagram<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">3. \u2220MRL and \u2220MRS are supplementary.<\/td>\n<td width=\"312\">3. Linear Pair Postulate (Postulate 2.8)<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">4. \u2220MRL \u2245 \u2220NSR<\/td>\n<td width=\"312\">4. Congruent Supplements Theorem (Theorem 2.4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u2220PSK\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2220KSN\u00a0 \u00a0 \u00a0 \u00a0 \u2220PSR\u00a0 \u00a0 \u00a0 \u00a0\u2220QRS\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2220QRL<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nYour teacher assigns your class a homework problem that asks you to prove the Vertical Angles Congruence Theorem (Theorem 2.6) using the picture and information given at the right. Your friend claims that this can be proved without using the Linear Pair Postulate (Postulate 2.8). Is our friend correct? Explain your reasoning.<br \/>\nGiven \u22201 and \u22203 arc vertical angles.<br \/>\nProve \u22201 \u2245 \u22203<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Geometry-Chapter-2-Reasoning-and-Proofs-156.png\" alt=\"Big Ideas Math Answers Geometry Chapter 2 Reasoning and Proofs 156\" width=\"242\" height=\"263\" \/><br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Reasoning and Proofs Chapter Answers provided are aligned as per the Big Ideas Math Geometry Textbooks. Have an overview of the concepts you need to learn in BIM Geometry Ch 2 Reasoning and Proofs and test your understanding. 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