Warm UpSolve.

1. x + 30 = 90

2. 103 + x = 180

3. 32 + x = 180

4. 90 = 61 + x

5. x + 20 = 90

Course 3

7-1 Points, Lines, Planes, and Angles

x = 60

x = 77

x = 148

x = 29

x = 70

Problem of the Day Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza?

Course 3

7-1 Points, Lines, Planes, and Angles

1

6

13

Learn to classify and name figures.

Course 3

7-1 Points, Lines, Planes, and Angles

TB P. 324-328

Vocabularypoint line plane

segment ray angle

right angle acute angle

obtuse angle complementary angles

supplementary angles

vertical angles

congruent

Insert Lesson Title Here

Course 3

7-1 Points, Lines, Planes, and Angles

Course 3

7-1 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.

Course 3

7-1 Points, Lines, Planes, and Angles

A point names a location.

• A Point A

Course 3

7-1 Points, Lines, Planes, and Angles

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

line l, or BCB

Cl

Course 3

7-1 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

Course 3

7-1 Points, Lines, Planes, and Angles

G

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

GH

Course 3

7-1 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

Course 3

7-1 Points, Lines, Planes, and Angles

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

A. Name 4 points in the figure.

B. Name a line in the figure.

Point J, point K, point L, and point M

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

Course 3

7-1 Points, Lines, Planes, and Angles

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

C. Name a plane in the figure.

Plane , plane JKL Any 3 points in the plane that form a triangle can be used.

Course 3

7-1 Points, Lines, Planes, and Angles

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

D. Name four segments in the figure.

E. Name four rays in the figure.KJ, KL, JK, LK

JK, KL, LM, JM

Course 3

7-1 Points, Lines, Planes, and Angles

An angle () is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees.

One degree, or 1°, is of a circle. m1

means the measure of 1. The angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter.

1360

X

Y Z1 m1 = 50°

Course 3

7-1 Points, Lines, Planes, and Angles

The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°.

F K J

G H

Course 3

7-1 Points, Lines, Planes, and Angles

The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360°.

P

R QM

N

Course 3

7-1 Points, Lines, Planes, and Angles

A right angle measures 90°.

An acute angle measures less than 90°.

An obtuse angle measures greater than 90° and less than 180°.

Complementary angles have measures that add to 90°.

Supplementary angles have measures that add to 180°.

Course 3

7-1 Points, Lines, Planes, and Angles

A right angle can be labeled with a small box at the vertex.

Reading Math

Course 3

7-1 Points, Lines, Planes, and Angles

Additional Example 2: Classifying Angles

A. Name a right angle in the figure.

B. Name two acute angles in the figure.

TQS

TQP, RQS

Course 3

7-1 Points, Lines, Planes, and Angles

Additional Example 2: Classifying Angles

C. Name two obtuse angles in the figure.

SQP, RQT

Course 3

7-1 Points, Lines, Planes, and Angles

Additional Example 2: Classifying Angles

D. Name a pair of complementary angles.

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

Course 3

7-1 Points, Lines, Planes, and Angles

Additional Example 2: Classifying Angles

E. Name two pairs of supplementary angles.

TQP, RQT

SQP, SQR

mTQP + mRQT = 47° + 133° = 180°

mSQP + mSQR = 137° + 43° = 180°

Course 3

7-1 Points, Lines, Planes, and Angles

Congruent figures have the same size and shape.

• Segments that have the same length are congruent.

• Angles that have the same measure are congruent.

• The symbol for congruence is , which is read “is congruent to.”

Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example.

Course 3

7-1 Points, Lines, Planes, and Angles

Additional Example 3A: Finding the Measure of Vertical Angles

In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

If m1 = 37°, find m3.

The measures of 1 and 2 are supplementary.

The measures of 2 and 3 are supplementary.

m2 = 180° – 37° = 143°

m3 = 180° – 143° = 37°

So m1 = m3 or m1 = m3. ~

Course 3

7-1 Points, Lines, Planes, and Angles

Additional Example 3B: Finding the Measure of Vertical Angles

In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

If m4 = y°, find m2.

m3 = 180° – y°

m2 = 180° – (180° – y°)

= 180° – 180° + y°

= y°

Distributive Property m2 = m4

So m4 = m2 or m4 m2.

Course 3

7-1 Points, Lines, Planes, and Angles

Lesson QuizIn the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

1. Name three points in the figure.

3. Name a right angle in the figure.

4. Name a pair of complementary angles.

5. If m1 = 47°, then find m3.

2. Name two lines in the figure.

Possible answer: A, B, and C

Possible answer: AGF

Possible answer: 1 and 2

47°

Possible answer: AD and BE