Chapter 3 Lesson Chapter 3 Lesson 22

Objective:Objective: To use a transversal in proving lines

parallel.

Postulate 3-2:Postulate 3-2:

Converse of the Corresponding Angles Postulate

If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

Theorem 3-3:Theorem 3-3:

Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

l

m

11

22l ml m

l

m11

2244

If 1 2, then l m.

Theorem 3-4:Theorem 3-4:

Converse of the Same-Side Interior Angles Theorem

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. If 2 and 4 are

supplementary, then l m

l

m11

2244

Example 1:Example 1:Proving Theorem 3-3Proving Theorem 3-3

Statements Reasons

1.) 1.)

2.) 2.)

3.) 3.)

4.) 4.)

Given:Given: 1 2 1 2 Prove:Prove: l ml m

l

m11

22

33

1 21 2 1 31 3 3 23 2

l ml m

Given

Vertical angles are congruentTransitive Prop. Of Congruence

Postulate 3-2

Example 2:Example 2:Using Theorem 3-4Using Theorem 3-4

Which lines, if any, must be parallel if 1 2? Justify Which lines, if any, must be parallel if 1 2? Justify your answer with a theorem or postulate.your answer with a theorem or postulate.

EE

DD

CC

KK11

33

44

22

DE is parallel to KC by DE is parallel to KC by Theorem 3-3, the Theorem 3-3, the

Converse of Alternate Converse of Alternate Interior Angles Interior Angles

Theorem.Theorem.

Example 3:Example 3:Which lines, if any, must be parallel if 3 4? Justify Which lines, if any, must be parallel if 3 4? Justify your answer with a theorem or postulate.your answer with a theorem or postulate.

EE

DD

CC

KK11

33

44

22

EC is parallel to DK by EC is parallel to DK by Postulate 3-2, Converse Postulate 3-2, Converse

of Corresponding of Corresponding Angles Postulate.Angles Postulate.

Example 4:Example 4:Proof of Theorem 3-6Proof of Theorem 3-6

Statements Reasons

1.) 1.)

2.) 2.)

3.) 3.)

4.)

5.) r sr s

4.)

5.)

Given:Given: tstr ,

Prove:Prove: rr ss

s

r

Given

Given

All Right Angles are Congruent

Converse of Corresponding Angles Postulate

t

1

2

tr ts

Angles 1 & 2 are right angles Definition of Perpendicular lines

21

l

m (2x+6)(2x+6)

4040

Example 5:Example 5:Find the value of x for which l m.

Corresponding Angles

2x+6 = 40

2x=34

x=17

Assignment:Assignment:

pg.125-127 #1-35

DUE Monday