# Texas Go Math Grade 4 Lesson 13.1 Answer Key Lines, Rays, and Angles

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## Texas Go Math Grade 4 Lesson 13.1 Answer Key Lines, Rays, and Angles

Essential Question

How can you identify and draw points, lines, line segments. rays, and angles?

Unlock the Problem

Everyday things can model geometric figures. For example, the period at the end of this sentence models a point. A solid painted stripe in the middle of a straight road models a line.

Activity 1 Draw and label $$\overline{J K}$$.
I have drawn and labeled $$\overline{J K}$$.

Explanation:

Math Talk

Mathematical Processes
Explain how lines, line segments, and rays are related.
A ray is a part of a line.
A line segment can be a part of a line, ray, or another line segment.

Explanation:

Ray AB = $$\overline{A B}$$

The line CD = $$\overline{C D}$$ or line DC = $$\overline{D C}$$.
From this we get $$\overline{C D}$$ or $$\overline{D C}$$.
From the above segment AB = $$\overline{A B}$$, segment BA = $$\overline{B A}$$
segment CD = $$\overline{C D}$$ and segment DC = $$\overline{D C}$$

Is there another way to name $$\overline{J K}$$? Explain.
Yes

Explanation:
Yes, there is a way to name $$\overline{J K}$$ by switching the letters, $$\overline{K J}$$ and when we are naming a line segment, either point can be named first.

Angles

You can name an angle by the vertex. When you name an angle using 3 points, the vertex is always the point in the middle.
We cannot say âˆ B here because that could be one of three angles. So we have to use either âˆ ABD or âˆ ABC, or âˆ DBC. We need to remember when we name an angle using 3 points, the vertex is always the point in the middle.

Explanation:

Angles are classified by the size of the opening between the rays.

Activity 2 Classify an angle.

Materials
paper

To classify an angle, you can compare it to a right angle.

Make a right angle by using a sheet of paper. Fold the paper twice evenly to model a right angle. Use the right angle to classify the angles below. Write acute, obtuse, right, or straight.

a.

Obtuse

Explanation:
An angle that measures greater than 90Â° degrees is called an obtuse angle.

b.

Acute

Explanation:
An angle that measures less than 90Â° degrees is called an acute angle.

c.

Acute

Explanation:
An angle that measures less than 90Â° degrees is called an acute angle.

d.

Right

Explanation:
The given angle is a right-angled triangle that has 90Â°

Share and Show

Draw and label $$\overline{A B}$$ in the space at the right.
$$\overline{A B}$$ is a _________________ .
Line segment

Explanation:

Draw and label an example of the figure.

Question 2.
$$\overleftrightarrow{X Y}$$
I have drawn and labeled an example of the figure to the given question

Explanation:

Question 3.
obtuse âˆ K
I have drawn and labeled an example of the figure to the given question

Explanation:

Question 4.
right âˆ CDE
I have drawn and labeled an example of the figure to the given question

Explanation:

Use Figure M for 5 and 6.

Question 5.
Name a line segment.
$$\overline{T U}$$

Go Math 4th Grade Answer Key Lines Rays and Angles Question 6.
Name a right angle.

âˆ TUW

Explanation:
By using the figure given above the name of the right angle is âˆ TUW.

Problem Solving

Lise the picture of the bridge for 7 and 8.

Question 7.
Classify âˆ A.
Right

Question 8.
Which angle appears to be obtuse?
âˆ C

Explanation:
The angle C appears to be obtuse.

Question 9.

H.O.T. Use Diagrams How many different angles are in Figure X? List them.

There are 10 different angles.

Explanation:
The different angles that are in Figure X are âˆ ABD, âˆ DBE, âˆ EBF, âˆ FBC, âˆ ABE, âˆ DBF, âˆ EBC, âˆ ABF, âˆ DBC, âˆ ABC.

Question 10.
H.O.T. Multi-Step Whatâ€™s the Error? Vanessa drew the angle at the right and named it âˆ  TRS. Explain why Vanessaâ€™s name for the angle is incorrect. Write a correct name for the angle.

âˆ TSR or âˆ RST

Explanation:
The vertex should be the middle letter in the angle’s name. The correct name for the angle is âˆ TSR or âˆ RST.

Question 11.
What type of angle is âˆ  ABC?

(A) acute
(B) right
(C) obtuse
(D) straight
Obtuse

Explanation:
The âˆ  ABC is a type of obtuse angle.

Texas Go Math Grade 4 Volume 1 Pdf Lesson 13.1 Question 12.
Which name is a straight angle in the figure below?

(A) âˆ  XTW
(B) âˆ  STX
(C) âˆ STY
(D) âˆ WTS
âˆ WTS

Explanation:
The âˆ WTS names a straight angle in the given figure.

Question 13.
Multi-Step What is the total number of acute angles in the figures shown below?

(A) 2
(B) 8
(C) 4
(D) 6
2

Explanation:
The total number of acute angles in the figures shown is 2.

TEXAS Test Prep

Question 14.
Which of the following terms best describes the figure below?

(A) ray
(B) line segment
(C) line
(D) angle
Ray

Explanation:
Ray is the term best describes the given figure.

### Texas Go Math Grade 4 Lesson 13.1 Homework and Practice Answer Key

Draw and label an example of the figure.

Question 1.
$$\overrightarrow{A B}$$

acute âˆ J

Question 3.
right âˆ ABC

Question 4.
$$\overleftrightarrow{J K}$$

Question 5.
obtuse âˆ XYZ

Question 6.
$$\overline{P Q}$$

Use figure A for 7 and 8.

Question 7.
Name an acute angle.

Explanation:
The name of an acute angle is âˆ BAD

Question 8.
Name an obtuse angle.
âˆ CDA

Explanation:
The name of an obtuse angle is âˆ CDA

Problem Solving

Use the bridge drawing for 9 and 10.

Question 9.
Classify âˆ B
Acute angle

Explanation:
Here the âˆ B is an acute angle that is below 90Â°.

Jenny thinks that âˆ C is a right angle. Explain why Jennyâ€™s name for the angle is incorrect. Write the correct name for the angle.
Obtuse angle

Explanation:
The correct name of the angle is an obtuse angle that has above 90Â°. Therefore what Jenny thinks is wrong and the angle is incorrect.

Lesson Check

Question 11.
What type of angle is âˆ XYZ?

(A) right
(B) acute
(C) straight
(D) obtuse
Acute

Explanation:
The âˆ XYZ is an acute angle.

Question 12.
Which names an obtuse angle in the figure below?

(A) âˆ TZS
(B) âˆ SZY
(C) âˆ XZT
(D) âˆ TZY
âˆ TZY

Explanation:
The âˆ TZY names an obtuse angle in the given figure.

Question 13.
Which names an acute angle in the figure to the right?

(A) âˆ  VWU
(B) âˆ  VTU
(C) âˆ  TUW
(D) âˆ  WUT
âˆ  VWU

Explanation:
The âˆ  VWU names an acute angle in the figure to the right.

Question 14.
Which of the following terms best describes the figure below?

(A) angle
(B) line segment
(C) ray
(D) line
line segment

Explanation:
The line segment term best describes the given figure.

Multi-Step What is the total number of rays in the figures to the right?

(A) 6
(B) 2
(C) 5
(D) 7
2

Explanation:
The total number of rays in the figure to the right is 2.

Question 16.
Multi-Step How many right angles are in Figure X?

(A) 4
(B) 2
(C) 3
(D) 1