Eureka Math Grade 7 Module 6 Lesson 7 Answer Key

Engage NY Eureka Math 7th Grade Module 6 Lesson 7 Answer Key

Eureka Math Grade 7 Module 6 Lesson 7 Example Answer Key

Example 1.
Use what you know about drawing parallel lines with a setsquare to draw rectangle ABCD with dimensions of your choice. State the steps you used to draw your rectangle, and compare those steps to those of a partner.
Answer:
Possible steps: Draw \(\overline{A B}\) first. Align the setsquare so that one leg aligns with \(\overline{A B}\), and place the ruler against the other leg of the setsquare; mark a point X, ___ cm away from \(\overline{A B}\). Draw a line parallel to \(\overline{A B}\) through X. Realign the setsquare with \(\overline{A B}\) situate the ruler so that it passes through A, and draw a segment with a length of ___ cm. Mark the intersection of the line through A and the parallel line to \(\overline{A B}\) as D. \(\overline{A D}\) is now drawn perpendicular to \(\overline{A B}\). Repeat the steps to determine C.

Example 2.
Use what you know about drawing parallel lines with a setsquare to draw rectangle ABCD with AB = 3 cm and BC = 5 cm. Write a plan for the steps you will take to draw ABCD.
Engage NY Math 7th Grade Module 6 Lesson 7 Example Answer Key 1
Answer:
Draw \(\overline{A D}\) first. Align the setsquare so that one leg aligns with \(\overline{A D}\), and place the ruler against the other leg of the setsquare; mark a point X 5 cm away from \(\overline{A D}\). Slide the setsquare along the ruler until it aligns with X. Draw a line parallel to \(\overline{A D}\) through X. To create the right angle at A, align the setsquare so that the leg of the setsquare aligns with \(\overline{A D}\), situate the ruler so that the outer edge of the ruler passes through A, and draw a line through A. Mark the intersection of the line through A and the parallel line to \(\overline{A D}\) as D. Repeat the steps to determine C.

Example 3.
Use a setsquare, ruler, and protractor to draw parallelogram PQRS so that the measurement of ∠P is 50°, PQ = 5 cm, the measurement of ∠Q is 130°, and the length of the altitude to \(\overline{P Q}\) is 4 cm.
Answer:
Steps to draw the figure: Draw \(\overline{P Q}\) first. Align the setsquare and ruler so one leg of the setsquare aligns with \(\overline{P Q}\), and mark a point X 4 cm from \(\overline{P Q}\). Slide the setsquare along the ruler so that one side of the setsquare passes through X, and draw a line through X; this line is parallel to \(\overline{P Q}\). Using \(\overline{P Q}\) as one ray of ∠P, draw ∠P so that the measurement of ∠P is 50° and that the ray PS intersects with the line parallel to \(\overline{P Q}\) (the intersection is S). Draw ∠Q so that the measurement of ∠Q is 130°; the ray QR should be drawn to intersect with the line parallel to \(\overline{P Q}\)(the intersection is R).
Engage NY Math 7th Grade Module 6 Lesson 7 Example Answer Key 2

Example 4.
Use a setsquare, ruler, and protractor to draw rhombus ABCD so that the measurement of ∠A = 80°, the measurement of ∠B = 100°, and each side of the rhombus measures 5 cm.
Answer:
Steps to draw the figure: Draw \(\overline{A B}\) first. Using \(\overline{A B}\) as one ray of ∠A, draw ∠A so that the measurement of ∠A is 80°. The other ray, or the to-be side of the rhombus, AD, should be 5 cm in length; label the endpoint of the segment as D. Align the setsquare and ruler so one leg of the setsquare aligns with \(\overline{A B}\) and the edge of the ruler passes through D. Slide the setsquare along the ruler so that the edge of the setsquare passes through D, and draw a line along the edge of the setsquare. This line is parallel to \(\overline{A B}\).

Now align the setsquare and ruler so one leg of the setsquare aligns with \(\overline{A D}\) and the edge of the ruler passes through B. Slide the setsquare along the ruler so that the edge of the setsquare passes through B, and draw a line along the edge of the setsquare. This line is parallel to \(\overline{A D}\). Along this line, measure a segment 5 cm with B as one endpoint, and label the other endpoint C. Join C to D.
Engage NY Math 7th Grade Module 6 Lesson 7 Example Answer Key 3

Eureka Math Grade 7 Module 6 Lesson 7 Exercise Answer Key

Exercise 1.
Use a setsquare, ruler, and protractor to draw parallelogram DEFG so that the measurement of ∠D is 40°, DE = 3 cm, the measurement of ∠E is 140°, and the length of the altitude to \(\overline{D E}\) is 5 cm.
Answer:
Steps to draw the figure: Draw \(\overline{D E}\) first. Align the setsquare and ruler so one leg of the setsquare aligns with \(\overline{D E}\) , and mark a point X 5 cm from \(\overline{D E}\) . Slide the setsquare along the ruler so that one side of the setsquare passes through X, and draw a line through X; this line is parallel to \(\overline{D E}\). Using \(\overline{D E}\) as one ray of ∠D, draw ∠D so that the measurement of ∠D is 40° and that the ray DG intersects with the line parallel to \(\overline{D E}\) (the intersection is G). Draw ∠E so that the measurement of ∠E is 140°; the ray EF should be drawn to intersect with the line parallel to \(\overline{D E}\) (the intersection is F).
Engage NY Math Grade 7 Module 6 Lesson 7 Exercise Answer Key 1

Eureka Math Grade 7 Module 6 Lesson 7 Problem Set Answer Key

Question 1.
Draw rectangle ABCD with AB = 5 cm and BC = 7 cm.
Answer:
Steps to draw the figure: Draw \(\overline{A B}\) first. Align the setsquare so that one leg aligns with \(\overline{A B}\), and place the ruler against the other leg of the setsquare; mark a point X 7 cm away from \(\overline{A B}\). Draw a line parallel to \(\overline{A B}\) through X. To create the right angle at A, align the setsquare so that its leg aligns with \(\overline{A B}\), situate the ruler so that the outer edge of the ruler passes through A, and draw a line through A. Mark the intersection of the line through A and the parallel line to \(\overline{A B}\) as D. Repeat the steps to determine C.

Question 2.
Use a setsquare, ruler, and protractor to draw parallelogram PQRS so that the measurement of ∠P is 65°, PQ = 8 cm, the measurement of ∠Q is 115°, and the length of the altitude to \(\overline{P Q}\) is 3 cm.
Answer:
Steps to draw the figure: Draw \(\overline{P Q}\) first. Align the setsquare and ruler so one leg of the setsquare aligns with \(\overline{P Q}\), and mark a point X 3 cm from \(\overline{P Q}\). Slide the setsquare along the ruler so that one side of the setsquare passes through X, and draw a line through X; this line is parallel to \(\overline{P Q}\). Using \(\overline{P Q}\) as one ray of ∠P, draw ∠P so that the measurement of ∠P is 65° and that the ray PS intersects with the line parallel to \(\overline{P Q}\) (the intersection is S). Draw ∠Q so that the measurement of ∠Q is 115°; the ray QR should be drawn to intersect with the line parallel to \(\overline{P Q}\) (the intersection is R).

Question 3.
Use a setsquare, ruler, and protractor to draw rhombus ABCD so that the measurement of ∠A is 60°, and each side of the rhombus measures 5 cm.
Answer:
Steps to draw the figure: Draw \(\overline{A B}\) first. Using \(\overline{A B}\) as one ray of ∠A, draw ∠A so that the measurement of
∠A is 60°. The other ray, or to-be side of the rhombus, AD, should be 5 cm in length; label the endpoint of the segment as D. Align the setsquare and ruler so one leg of the setsquare aligns with \(\overline{A B}\) and the edge of the ruler passes through D. Slide the setsquare along the ruler so that the edge of the setsquare passes through D, and draw a line along the edge of the setsquare.

This line is parallel to\(\overline{A B}\). Now, align the setsquare and ruler so one leg of the setsquare aligns with \(\overline{A D}\) and the edge of the ruler passes through B. Slide the setsquare along the ruler so that the edge of the setsquare passes through B, and draw a line along the edge of the setsquare. This line is parallel to \(\overline{A D}\). Along this line, measure a segment 5 cm with B as one endpoint, and label the other endpoint C. Join C to D.

The following table contains partial information for parallelogram ABCD. Using no tools, make a sketch of the parallelogram. Then, use a ruler, protractor, and setsquare to draw an accurate picture. Finally, complete the table with the unknown lengths.
Two of the sketches are provided.
Eureka Math 7th Grade Module 6 Lesson 7 Problem Set Answer Key 2

The following table contains partial information for parallelogram ABCD. Using no tools, make a sketch of the parallelogram. Then, use a ruler, protractor, and setsquare to draw an accurate picture. Finally, complete the table with the unknown lengths.
Eureka Math 7th Grade Module 6 Lesson 7 Problem Set Answer Key 3
Answer:
Eureka Math 7th Grade Module 6 Lesson 7 Problem Set Answer Key 4

Question 7.
Use what you know about drawing parallel lines with a setsquare to draw trapezoid ABCD with parallel sides \(\overline{A B}\) and \(\overline{C D}\). The length of \(\overline{A B}\) is 3 cm, and the length of \(\overline{C D}\) is 5 cm; the height between the parallel sides is 4 cm. Write a plan for the steps you will take to draw ABCD.
Answer:
Draw \(\overline{A B}\) (or \(\overline{C D}\)) first. Align the setsquare and ruler so that one leg of the
setsquare aligns with \(\overline{A B}\); mark a point X 4 cm away from \(\overline{A B}\). Draw a line parallel to \(\overline{A B}\) through X. Once a line parallel to \(\overline{A B}\) has been drawn through X, measure a portion of the line to be 3 cm, and label the endpoint on the right as C and the other endpoint D. Join D to A and C to B.
Eureka Math 7th Grade Module 6 Lesson 7 Problem Set Answer Key 5

Question 8.
Use the appropriate tools to draw rectangle FIND with FI = 5 cm and IN = 10 cm.
Answer:
Draw \(\overline{F I}\) first. Align the setsquare so that one leg aligns with \(\overline{F I}\), and place the ruler against the other leg of the
setsquare; mark a point X 10 cm away from \(\overline{F I}\). Draw a line parallel to \(\overline{F I}\) through X. To create the right angle at F, align the setsquare so that its leg aligns with \(\overline{F I}\), and situate the ruler so that its outer edge passes through F, and then draw a line through F. Mark the intersection of the line through F and the parallel line to \(\overline{F I}\) as D. Repeat the steps to determine N.

Question 9.
Challenge: Determine the area of the largest rectangle that will fit inside an equilateral triangle with side length 5 cm.
Answer:
Students will quickly discover that rectangles of different dimensions can be drawn; finding the largest rectangle may take multiple efforts. The maximum possible area is 5.4 cm2.

Eureka Math Grade 7 Module 6 Lesson 7 Exit Ticket Answer Key

Use what you know about drawing parallel lines with a setsquare to draw square ABCD with AB = 5 cm. Explain how you created your drawing.
Answer:
Draw \(\overline{A B}\)(any side will do here) first. Align the setsquare and ruler so that one leg of the setsquare aligns with \(\overline{A B}\); mark a point X 5 cm away from \(\overline{A B}\). Draw a line parallel to \(\overline{A B}\) through X. To create the right angle at A, align the setsquare so that the leg of the setsquare aligns with \(\overline{A B}\), situate the ruler so that the outer edge of the ruler passes through A, and draw a line through A. Mark the intersection of the line through A and the parallel line to \(\overline{A B}\) as D; join A and D. Repeat the steps to determine C, and join B and C.
Eureka Math Grade 7 Module 6 Lesson 7 Exit Ticket Answer Key 1

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