13.1 Lines, Rays, and Angles

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Unlock the Problem

F G

D E

B C

A

Mathematical Processes

Math Talk

Explain how lines, line segments, and rays

are related. Essential Question

?

Name Geometry and Measurement—4.6.A MATHEMATICAL PROCESSES 4.1.D, 4.1.E

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

13.1

Lines, Rays, and Angles

Activity 1

Draw and label ___JK .

____

Term and Definition Draw It Read It Write It Example

A point is an exact location in

space. point A point A

A line is a straight path of points that continues without end in both directions. line BC line CB ‹__› BC ‹__› CB

A line segment is part of a line

between two endpoints. line segment _{line segment}DE_ED

___ DE

___ ED

A ray is a part of a line that has one endpoint and continues without end in one direction.

ray FG __FG› 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.

• Is there another way to name JK ___ ? Explain.

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Q

P

R

a. b. c. d.

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.

Term and Definition Draw It Read It Write It Example

An angle is formed by two rays or line segments that have the same endpoint. The shared endpoint is called the vertex.

angle PQR angle RQP angle Q ∠PQR ∠RQP ∠Q

Angles

A right angle forms a square corner.

A straight angle forms a line.

An acute angle is less than a right angle.

An obtuse angle is greater than a right angle and less than a straight angle. 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. Angles are classified by the size of the opening between the rays.

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Share and Show

T U V W Figure M

Problem Solving

S R T A C F D E B Figure X Name

5. Name a line segment. 6. Name a right angle.

2. ‹___XY › _3._obtuse_∠_K _4._right_∠_CDE

Use Figure M for 5 and 6.

Draw and label an example of the figure.

1. Draw and label AB ___ in the space at the right. AB ___ is a

____

.

7. Classify ∠A. 8. Which angle appears to be obtuse?

9. Use Diagrams How many different angles are in Figure X? List them.

10. Multi-Step What’s the Error? Vanessa drew the angle at the right and named it ∠TRS. Explain why Vanessa’s name for the angle is incorrect. Write a correct name for the angle.

Use the picture of the bridge for 7 and 8.

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Mathematical Processes

Model ¥ Reason ¥ Communicate

M

Daily Assessment Task

Z Y X S T A D B C A B Y W X S T C B A

TEXAS Test Prep

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

A ray C line

Fill in the bubble completely to show your answer. 11. What type of angle is ∠ABC?

A acute B right C obtuse D straight

12. Which names a straight angle in the figure below?

A ∠XTW C ∠STY

B ∠STX D ∠WTS

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

A 2 C 4

B 8 D 6

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Problem Solving

A D B C Figure A

Homework

and Practice

Name

Geometry and Measurement—4.6.A

MATHEMATICAL PROCESSES 4.1.D, 4.1.E

13.1

Lines, Rays, and Angles

9. Classify ∠B

10. Jenny thinks that ∠C is a right angle. Explain

why Jenny’s name for the angle is incorrect. Write a correct name for the angle.

Draw and label an example of the figure.

Use figure A for 7 and 8.

Use the bridge drawing for 9 and 10.

1. ___AB › 2. acute ∠J 3. right _∠ABC

7. Name an acute angle. 8. Name an obtuse angle.

4. ‹JK __› 5. obtuse ∠XYZ 6. ___PQ

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TEXAS Test Prep

Lesson Check

Y X Z Z Y X S T A B T U V W Figure M A D B C Y W X S T A C F D E B Figure X Fill in the bubble completely to show your answer.

11. What type of angle is ∠XYZ?

A right

B acute

C straight

D obtuse

12. Which names an obtuse angle in the

figure below?

A ∠TZS

B ∠SZY

C ∠XZT

D ∠TZY

13. Which names an acute angle

in the figure to the right?

A ∠VWU

B ∠VTU

C ∠TUW

D ∠WUT

14. Which of the following terms best

describes the figure below?

A angle

B line segment

C ray

D line

15. Multi-Step What is

the total number of rays in the figures to the right?

A 6

B 2

C 5

D 7

16. Multi-Step How

many right angles

are in Figure X? A 4 B 2 C 3 D 1 Publishing Compan y