UNIT 3.1 LINES AND UNIT 3.1 LINES AND

ANGLESANGLES

Warm UpIdentify 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

Identify parallel, perpendicular, and skew lines.

Identify the angles formed by two lines and a transversal.

Objectives

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

Vocabulary

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

Helpful Hint

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

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

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

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

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

Helpful Hint

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

Check It Out! Example 3

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

transversal nsame-side int. ∠s.

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

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

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