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Additional Example 2: Classifying Angles geometry. Segments, rays, and angles are defined in terms of these basic figures.

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

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.

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.point names a location.

• A

Point A

C geometry. Segments, rays, and angles are defined in terms of these basic figures.

l

B

line l, or BC

A line is perfectly straight and extends forever in both directions.

A geometry. Segments, rays, and angles are defined in terms of these basic figures.plane is a perfectly flat surface that extends forever in all directions.

P

E

plane P, or plane DEF

D

F

GH geometry. Segments, rays, and angles are defined in terms of these basic figures.

A segment, or line segment, is the part of a line between two points.

H

G

A geometry. Segments, rays, and angles are defined in terms of these basic figures.ray is a part of a line that starts at one point and extends forever in one direction.

J

KJ

K

KL geometry. Segments, rays, and angles are defined in terms of these basic figures. 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 geometry. Segments, rays, and angles are defined in terms of these basic figures.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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

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! geometry. Segments, rays, and angles are defined in terms of these basic figures.

When naming a ray always write the endpoint first.

AB, BC, CD, AD geometry. Segments, rays, and angles are defined in terms of these basic figures.

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

Use the diagram to name each figure.

A. a right angle

TQS

B. two acute angles

TQP, RQS

Reading Math geometry. Segments, rays, and angles are defined in terms of these basic figures.

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

Additional Example 2: Classifying Angles geometry. Segments, rays, and angles are defined in terms of these basic figures.

Use the diagram to name each figure.

C. two obtuse angles

SQP, RQT

Additional Example 2: Classifying Angles geometry. Segments, rays, and angles are defined in terms of these basic figures.

Use the diagram to name each figure.

D. a pair of complementary angles

TQP, RQS

mTQP + mRQS = 47° + 43° = 90°

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

A. a right angle

BEC

C geometry. Segments, rays, and angles are defined in terms of these basic figures.

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

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 geometry. Segments, rays, and angles are defined in terms of these basic figures.

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: geometry. Segments, rays, and angles are defined in terms of these basic figures.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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