Corresponding Angles Postulate

• If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

1

2

1 ≅ 2

Alternate Interior Angles

• If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

3

4

3 ≅ 4

Consecutive Interior Angles

• If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

5

6

5 + 6 = 180°

Alternate Exterior Angles

• If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

7

8

7 ≅ 8

Perpendicular Transversal• If a transversal is perpendicular to one of

the two parallel lines, then it is perpendicular to the other.

j k

jh

k

State the postulate or theorem that justifies the statement.

>

>ab

c d

efgh

ha .1

ec .2

180.3 ed

fb .4

EXAMPLE 1 Review

EXAMPLE 2 Prove the Alternate Interior Angles Converse

SOLUTION

GIVEN : 4 5

PROVE : g h

EXAMPLE 2 Prove the Alternate Interior Angles Converse

1. Given

g h4.

1. 4 5

2. 1 4

3. 1 5

2. Vertical Angles Congruence Theorem

3. Transitive Property of Congruence

4. Corresponding Angles Converse

STATEMENTS REASONS

EXAMPLE 3 Prove the Alternate Interior Angles Theorem

GIVEN : p q

PROVE :1 2

EXAMPLE 3 Prove the Alternate Interior Angles Converse

1. Given1.

2. 3 2

3. 1 3

2. Vertical Angles

3. Corresponding Angles

4. Transitive Property

STATEMENTS REASONS

p q

4. 1 2

EXAMPLE 4 Write a paragraph proof

Given: r s and 1 is congruent to 3.

Prove: p q.

EXAMPLE 3

1. Givenr s1.

3. 1 3

4. 2 3

2. 1 2

4. Substitution

3. Given

2. Corresponding Angles

STATEMENTS REASONS

p q5 5. Alternate Interior Angles

Given: m || n, n || kProve: m || k

Statements Reasons

1. m || n 1. Given

2. 2. Corresponding

3. n || k 3. Given

4. 4. Corresponding

5. 5. Transitive

6. m || k 6.Corresponding

21

32

m

n

k

1

2

3

31

EXAMPLE 4

EXAMPLE 3EXAMPLE 3

REASONSSTATEMENTS

Given: l m, & t l, Proof: t m.

1

2

l

m

t

Statements

1. l m, t l 2. 12

3. m1=m2

4. 1 is a rt. 5. m1=90o

6. 90o=m2

7. 2 is a rt. 8. t m

Reasons

1. Given

2. Corresponding angles

3. Def of s

4. Def of lines

5. Def of rt. 6. Substitution

7. Def of rt. 8. Def of lines