Holt McDougal Geometry 3-1 Lines and Angles Warm Up Identify each of the following. 1. points that lie in the same plane 2.two angles whose sum is 180°

Holt McDougal Geometry

3-1 Lines and Angles

Warm Up

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



Identify parallel, perpendicular, and skew lines.

Identify the angles formed by two lines and a transversal.

Objectives





Example 1: Identifying Types of Lines and Planes


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


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











Students will…

Use the angles formed by a transversal to prove two lines are

parallel.

Objective



Remember!

Converse of a theorem is found by exchanging the hypothesis and

conclusion.

***The converse of a theorem is not automatically true.

If it is true, it must be stated as a postulate or proved as a separate

theorem.







Use the given information and the theorems you have learned to show that r || s.

4 8

4 8 4 and 8 are alternate exterior angles.

r || s Conv. Of Alt. Ext. s Thm.



Use the given information and the postulates you have learned to show that l || m.

1 3 1 and 3 are corresponding angles.

ℓ || m Conv. of Corr. s Post.



Which postulate proves that ℓ || m?

m3 = (4x – 80)°,

m7 = (3x – 50)°, x = 30

m3 = 4(30) – 80 = 40 Substitute 30 for x.m7 = 3(30) – 50 = 40 Substitute 30 for x.

ℓ || m Conv. of Corr. s Post.3 7 Def. of s.

m3 = m7









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Holt McDougal Geometry 3-1 Lines and Angles Warm Up Identify each of the following. 1. points that lie in the same plane 2.two angles whose sum is 180°