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Warm Up

Solve.

1. x + 30 = 90

2. 103 + x = 180

3. 32 + x = 180

4. 90 = 61 + x

5. x + 20 = 90

x = 60

x = 77

x = 148

x = 29

x = 70

California

Standards

Preparation for MG3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

Vocabulary

point line plane

segment ray angle

right angle

acute angle

obtuse angle

straight angle

complementary angles

supplementary angles

Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

A plane is a perfectly flat surface that extends forever in all directions.

P

E

plane P, or plane DEF

D

F

KL or JK

Additional Example 1: Naming Lines, Planes, Segments, and Rays

Use the diagram to name each figure.

A. a line

Possible answers:

Any 2 points on a line can be used.

Plane or plane JKL

Additional Example 1: Naming Lines, Planes, Segments, and Rays

Use the diagram to name each figure.

B. a plane

Possible answers:

Any 3 points in the plane that form a triangle can name a plane.

JK, KL, LM, JM

KJ, KL, JK, LK

Additional Example 1: Naming Lines, Planes, Segments, and Rays

Use the diagram to name each figure.

C. four segments

Possible answers:

Write the two points in any order.

D. four rays

Possible answers:

Write the endpoint first.

Caution!

When naming a ray always write the endpoint first.

AB, BC, CD, AD

B

A

C

D

CB, CD, DA, DC

Check It Out! Example 1

Use the diagram to name each figure.

A. four segments

Possible answers:

Write the two points in any order.

B. four rays

Possible answers:

Write the endpoint first.

B

A

AB or DC

C

D

Check It Out! Example 1

Use the diagram to name each figure.

C. a line

Possible answers:

Any 2 points on a line can be used.

B

A

C

D

Check It Out! Example 1

Use the diagram to name each figure.

D. a plane

Possible answers:

Any 3 points in the plane that form a triangle can name a plane.

Plane R or plane ABC

1

360

An angle () is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex.

Angles are usually measured in degrees ((°). Since

there are 360° in a circle, one degree is of a circle.

Additional Example 2: Classifying Angles

Use the diagram to name each figure.

A. a right angle

TQS

B. two acute angles

TQP, RQS

Reading Math

mTQS is read as “the measure of angle TQS.”

Additional Example 2: Classifying Angles

Use the diagram to name each figure.

C. two obtuse angles

SQP, RQT

Additional Example 2: Classifying Angles

Use the diagram to name each figure.

D. a pair of complementary angles

TQP, RQS

mTQP + mRQS = 47° + 43° = 90°

Additional Example 2: Classifying Angles

Use the diagram to name each figure.

E. two pairs of supplementary angles

TQP, RQT

mTQP + mRQT = 47° + 133° = 180°

mSQP + mSQR = 137° + 43° = 180°

SQP, SQR

C

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

B. two acute angles

AEB, CED

C. two obtuse angles

BED, AEC

C

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

D. a pair of complementary angles

mAEB + mCED = 15° + 75° = 90°

AEB, CED

C

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

E. two pairs of supplementary angles

mAEB + mBED = 15° + 165° = 180°

AEB, BED

mCED + mAEC = 75° + 105° = 180°

CED, AEC

Possible answer: AD and BE

Lesson Quiz

1. Name two lines in the figure.

2. Name a right angle in the figure.

Possible answer: AGF

3. Name a pair of complementary angles.

Possible answer: 1 and 2

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