## Engage NY Eureka Math 4th Grade Module 4 Lesson 1 Answer Key

### Eureka Math Grade 4 Module 4 Lesson 1 Problem Set Answer Key

Question 1.

Use the following directions to draw a figure in the box to the right.

a. Draw two points: A and B.

b. Use a straightedge to draw \(\overline{A B}\).

c. Draw a new point that is not on \(\overline{A B}\). Label it C.

d. Draw \(\overline{A C}\).

e. Draw a point not on \(\overline{A B}\) or \(\overline{A C}\). Call it D.

f. Construct

g. Use the points you’ve already labeled to name one angle. ____________

Answer:

The labeled angle is <ACD/<BAC.

Explanation:

Here, we have to draw two points and then labeled them as A and B.

And used a straightedge to draw \(\overline{A B}\).

Then we have to draw a new point that is not on \(\overline{A B}\). And we will label it as C.

Then we will draw \(\overline{A C}\).

Then we will draw a point not on \(\overline{A B}\) or \(\overline{A C}\). And we will label it as D.

And then we will construct

We will use these points and we will label with one angle as <ACD/<BAC.

Question 2.

Use the following directions to draw a figure in the box to the right.

a. Draw two points: A and B.

b. Use a straightedge to draw \(\overline{A B}\).

c. Draw a new point that is not on \(\overline{A B}\). Label it C.

d. Draw \(\overline{B C}\).

e. Draw a new point that is not on \(\overline{A B}\) or \(\overline{A C}\)

Label it D.

f. Construct .

g. Identify ∠DAB by drawing an arc to indicate the position of the angle.

h. Identify another angle by referencing points that you have already drawn. _____________

Answer:

The labeled angle is <ABC.

Explanation:

Here, we have to draw two points and label them as A and B.

And use a straightedge to draw \(\overline{A B}\).

Then we have to draw a new point that is not on \(\overline{A B}\). Label it C.

Then we will draw \(\overline{B C}\).

And we will draw a new point that is not on \(\overline{A B}\) or \(\overline{A C}\)

Label it D.

So we will construct .

Then we have identified ∠DAB by drawing an arc to indicate the position of the angle.

And we have Identified another angle by referencing points that we have already drawn.

Question 3.

a. Observe the familiar figures below. Label some points on each figure.

b. Use those points to label and name representations of each of the following in the table below: ray, line, line segment, and angle. Extend segments to show lines and rays.

Extension: Draw a familiar figure. Label it with points, and then identify rays, lines, line segments, and angles as applicable.

Answer:

The ray of the house is marked as AB,

The ray of the flash drive is marked as CD,

The ray of the direction compass is marked as EF.

The Line of the house is marked as AB,

The Line of the flash drive is marked as CD,

The Line of the direction compass is marked as EF.

The Line segment of the house is marked as GH,

The Line segment of the flash drive is marked as IJ,

The Line segment of the direction compass is marked as EK.

The Angle of the house is marked as <HGA,

The Angle of the flash drive is marked as <CIJ,

The Angle of the direction compass is marked as <KEF.

Explanation:

Ray: A Ray can be defined as a part of the line which has a fixed starting point but does not have any endpoint and it can be extended infinitely in one direction and a ray may pass through more than one point.

The ray of the house is marked as AB,

The ray of the flash drive is marked as CD,

The ray of the direction compass is marked as EF.

Line: A line can be defined as a long, straight and continuous path which is represented using arrowheads at both directions and the lines that do not have a fixed point it can be extended in two directions.

The Line of the house is marked as AB,

The Line of the flash drive is marked as CD,

The Line of the compass rose is marked as EF.

Line segment: A line segment is a straight line that passes through the two points and has fixed point and it can not be extended.

The Line segment of the house is marked as GH,

The Line segment of the flash drive is marked as IJ,

The Line segment of the compass rose is marked as EK.

Angle: A figure which is formed by two rays or lines that shares a common endpoint and is called an angle.

So in the above, we can see the house, flash drive, and a compass rose.

The Angle of the house is marked as <HGA,

The Angle of the flash drive is marked as <CIJ,

The Angle of the compass rose is marked as <KEF.

### Eureka Math Grade 4 Module 4 Lesson 1 Exit Ticket Answer Key

Question 1.

Draw a line segment to connect the word to its picture.

Answer:

Ray: A Ray can be defined as a part of the line which has a fixed starting point but does not have any endpoint and it can be extended infinitely in one direction and a ray may pass through more than one point.

Line: A line can be defined as a long, straight and continuous path which is represented using arrowheads at both directions and the lines that do not have a fixed point it can be extended in two directions.

Line segment: A line segment is a straight line that passes through the two points and has fixed point and it can not be extended.

Point: A point is an exact location and it has no point only position and point can usually be named often with letters like A, B, etc.

Angle: A figure which is formed by two rays or lines that shares a common endpoint and is called an angle.

Explanation:

Ray: A Ray can be defined as a part of the line which has a fixed starting point but does not have any endpoint and it can be extended infinitely in one direction and a ray may pass through more than one point.

Line: A line can be defined as a long, straight and continuous path which is represented using arrowheads at both directions and the lines that do not have a fixed point it can be extended in two directions.

Line segment: A line segment is a straight line that passes through the two points and has fixed point and it can not be extended.

Point: A point is an exact location and it has no point only position and a point can usually be named often with letters like A, B, etc.

Angle: A figure which is formed by two rays or lines that shares a common endpoint and is called an angle.

Question 2.

How is a line different from a line segment?

Answer:

A line can be defined as a long, straight and continuous path which is represented using arrowheads in both directions and the lines do not have a fixed point it can be extended in two directions, but the line segment is a straight line that passes through the two points and have a fixed point and it can not be extended.

### Eureka Math Grade 4 Module 4 Lesson 1 Homework Answer Key

Question 1.

Use the following directions to draw a figure in the box to the right.

a. Draw two points: W and X.

b. Use a straightedge to draw \(\overline{W X}\).

c. Draw a new point that is not on \(\overline{W X}\). Label it Y.

d. Draw \(\overline{W Y}\).

e. Draw a point not on \(\overline{W X}\) or \(\overline{W Y}\). Call it Z.

f. Construct

g. Use the points you’ve already labeled to name one angle. ____________

Answer:

The labeled angle is <XWY.

Explanation:

Here, we will draw two points which are represented with W and X.

And we will use a straightedge to draw \(\overline{W X}\).

And then we will draw a new point that is not on \(\overline{W X}\). And we will label it as Y.

Then we will draw \(\overline{W X}\).

Next we will draw a point not on \(\overline{W X}\) or \(\overline{W Y}\). And we will call it Z.

And then we will construct

Then we will use these points which were already labeled and name the angle as <XWY.

Question 2.

Use the following directions to draw a figure in the box to the right.

a. Draw two points: W and X.

b. Use a straightedge to draw \(\overline{W X}\).

c. Draw a new point that is not on \(\overline{W X}\). Label it Y.

d. Draw \(\overline{W Y}\).

e. Draw a new point that is not on \(\overline{W Y}\) or on the line containing \(\overline{W X}\). Label it Z.

f. Construct .

g. Identify ∠ZWX by drawing an arc to indicate the position of the angle.

h. Identify another angle by referencing points that you have already drawn. _____________

Answer:

The identified angle is <XW.

Explanation:

Here, we will draw two points and will label them as W and X.

And we will use a straightedge to draw \(\overline{W X}\).

Now we need to draw a new point that is not on \(\overline{W X}\). Label it Y.

Then we will draw \(\overline{W Y}\).

Next, we will draw a new point that is not on \(\overline{W Y}\) or on the line containing \(\overline{W X}\) and Label it as Z.

Then we need to Construct .

And then we will identify the angle ∠ZWX by drawing an arc to indicate the position of the angle.

So we will Identify another angle by referencing points that we have already drawn and label the angle as <XW.

Question 3.

a. Observe the familiar figures below. Label some points on each figure.

b. Use those points to label and name representations of each of the following in the table below: ray, line, line segment, and angle. Extend segments to show lines and rays.

Extension: Draw a familiar figure. Label it with points, and then identify rays, lines, line segments, and angles as applicable.

Answer:

The ray of the clock is marked as AB,

The ray of the die is marked as EF,

The ray of the number line is marked as AC.

The Line of the clock is marked as BC,

The Line of the die is marked as FG,

The Line of the number line is marked as AB.

The Line segment of the clock is marked as AC,

The Line segment of the die is marked as GH,

The Line segment of the number line is marked as BD.

The Angle of the clock is marked as <CAB,

The Angle of the die is marked as <FGH

The Angle of the number line is marked as <CAB.

Explanation:

Ray: A Ray can be defined as a part of the line which has a fixed starting point but does not have any endpoint and it can be extended infinitely in one direction and a ray may pass through more than one point.

The ray of the clock is marked as AB,

The ray of the die is marked as EF,

The ray of the number line is marked as AC.

Line: A line can be defined as a long, straight and continuous path which is represented using arrowheads at both directions and the lines that do not have fixed points it can be extended in two directions.

The Line of the clock is marked as BC,

The Line of the die is marked as FG,

The Line of the number line is marked as AB.

Line segment: A line segment is a straight line that passes through the two points and has fixed point and it can not be extended.

The Line segment of the clock is marked as AC,

The Line segment of the die is marked as GH,

The Line segment of the number line is marked as BD.

Angle: A figure which is formed by two rays or lines that shares a common endpoint and is called an angle.

So in the above, we can see the clock, die, and a number line.

The Angle of the clock is marked as <CAB,

The Angle of the die is marked as <FGH

The Angle of the number line is marked as <CAB.