3-1 Lines and Angles

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Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

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Identify each of the following.

1. points that lie in the same plane

2. two angles whose sum is 180°

3. the intersection of two distinct intersecting lines

4. a pair of adjacent angles whose non-common sides are opposite rays

coplanar points

supplementary angles

point

linear pair

3.1 Lines and Angles

Identify parallel, perpendicular, and skew lines.

Identify the angles formed by two lines and a transversal.

Objectives

3.1 Lines and Angles

parallel linesperpendicular linesskew linesparallel planestransversalcorresponding anglesalternate interior anglesalternate exterior anglessame-side interior angles

Vocabulary

3.1 Lines and Angles

3.1 Lines and Angles

Segments or rays are parallel, perpendicular, or skew if the lines that contain them are parallel, perpendicular, or skew.

Helpful Hint

3.1 Lines and Angles

Example 1: Identifying Types of Lines and Planes

Identify each of the following.

A. a pair of parallel segments

B. a pair of skew segments

C. a pair of perpendicular segments

D. a pair of parallel planes

LM ||QR

KN and PQ

NS SP

plane NMR || plane KLQ

3.1 Lines and Angles

Check It Out! Example 1

Identify each of the following.

a. a pair of parallel segments

b. a pair of skew segments

d. a pair of parallel planes

c. a pair of perpendicular segments

BF || EJ

BF and DE are skew.

BF FJ

plane FJH || plane BCD

3.1 Lines and Angles

3.1 Lines and Angles

Example 2: Classifying Pairs of Angles

Give an example of each angle pair.

A. corresponding angles

B. alternate interior angles

C. alternate exterior angles

1 and 5

D. same-side interior angles

3 and 5

1 and 7

3 and 6

3.1 Lines and Angles

Check It Out! Example 2

Give an example of each angle pair.

A. corresponding angles

B. alternate interior angles

C. alternate exterior angles

1 and 3

D. same-side interior angles

2 and 7

1 and 8

2 and 3

3.1 Lines and Angles

To determine which line is the transversal for a given angle pair, locate the line that connects the vertices.

Helpful Hint

3.1 Lines and Angles

Example 3: Identifying Angle Pairs and Transversals

Identify the transversal and classify each angle pair.

A. 1 and 3

B. 2 and 6

C. 4 and 6

transversal l corr. s

transversal nalt. int s

transversal malt. ext s

3.1 Lines and Angles

Check It Out! Example 3

Identify the transversal and classify the angle pair 2 and 5 in the diagram.

transversal nsame-side int. s.

3.1 Lines and Angles

Lesson Quiz: Part I

Identify each of the following.

1. a pair of parallel segments

2. a pair of skew segments

3. a pair of perpendicular segments

4. a pair of parallel planes

EH || FG

BF and EH

CG GH

ABC and EFG

3.1 Lines and Angles

Lesson Quiz: Part II

Identify each of the following.

5. one pair alternate interior angles

6. One pair corresponding angles

7. one pair alternate exterior angles

EHG and HGK

8. one pair same-side interior angles

EHG and FGJ

IHE and JGK

EHG and HGF

3.1 Lines and Angles