Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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.

California Standards

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

A point names a location.

• A Point A

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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

line l, or BCB

Cl

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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

plane P, or plane DEF

DE

F

PP

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

G

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

GH

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

K

JA ray is a part of a line that starts at one point and extends forever in one direction.

KJ

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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

A. a line

Any 2 points on a line can be used.KL or JK

Use the diagram to name each figure.

Possible answers:

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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

B. a plane

Use the diagram to name each figure.

Possible answers:

Plane or plane JKLAny 3 points in the plane that form a triangle can name a plane.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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

C. four segments

Use the diagram to name each figure.

Possible answers:

JK, KL, LM, JM

D. four rays

KJ, KL, JK, LK

Possible answers: Write the endpoint first.

Write the two points in any order.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

When naming a ray always write the endpoint first.

Caution!

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

Check It Out! Example 1

A. four segments

Use the diagram to name each figure.

Possible answers:

AB, BC, CD, AD

B. four rays

CB, CD, DA, DC

Possible answers:

A B

CD

Write the endpoint first.

Write the two points in any order.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

Check It Out! Example 1

C. a line

Any 2 points on a line can be used.AB or DC

Use the diagram to name each figure.

Possible answers:

A B

CD

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

Check It Out! Example 1

Use the diagram to name each figure.

Possible answers:

A B

CD

D. a plane

Plane R or plane ABCAny 3 points in the plane that form a triangle can name a plane.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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.

1360

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

Holt CA Course 1

8-1 Points, Lines, Planes, and AnglesAdditional Example 2: Classifying Angles

A. a right angle

B. two acute angles

TQS

TQP, RQS

Use the diagram to name each figure.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

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

Reading Math

Holt CA Course 1

8-1 Points, Lines, Planes, and AnglesAdditional Example 2: Classifying Angles

C. two obtuse angles

SQP, RQT

Use the diagram to name each figure.

Holt CA Course 1

8-1 Points, Lines, Planes, and AnglesAdditional Example 2: Classifying Angles

D. a pair of complementary angles

TQP, RQS mTQP + mRQS = 47° + 43° = 90°

Use the diagram to name each figure.

Holt CA Course 1

8-1 Points, Lines, Planes, and AnglesAdditional Example 2: Classifying Angles

E. two pairs of supplementary angles

TQP, RQT

SQP, SQR

mTQP + mRQT = 47° + 133° = 180°

mSQP + mSQR = 137° + 43° = 180°

Use the diagram to name each figure.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

Check It Out! Example 2

A. a right angle

BEC

E

D

CB

A 90° 75°15°

Use the diagram to name each figure.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

C. two obtuse angles

BED, AEC

B. two acute angles

AEB, CED

E

D

CB

A 90° 75°15°

Check It Out! Example 2

Use the diagram to name each figure.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

D. a pair of complementary angles

AEB, CED

E

D

CB

A 90° 75°15°

Check It Out! Example 2

mAEB + mCED = 15° + 75° = 90°

Use the diagram to name each figure.

Holt CA Course 1

8-1 Points, Lines, Planes, and Angles

E. two pairs of supplementary angles

AEB, BED

CED, AEC

E

D

CB

A 90° 75°15°

Check It Out! Example 2

mAEB + mBED = 15° + 165° = 180°

mCED + mAEC = 75° + 105° = 180°

Use the diagram to name each figure.