1. Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2
1 ≅ 2

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

3. 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°

4. 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

5. Perpendicular Transversal
If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other. j h k
j  k

6. State the postulate or theorem that justifies the statement.
EXAMPLE 1
Review
State the postulate or theorem that justifies the statement. b a
> c d f e
> g h

7. EXAMPLE 2
Prove the Alternate Interior Angles Converse
SOLUTION
GIVEN :
∠ ∠ 5
PROVE :
g h

8. Prove the Alternate Interior Angles Converse
EXAMPLE 2
Prove the Alternate Interior Angles Converse
STATEMENTS
REASONS 1.
4 ∠ 1.
Given 2.
Vertical Angles Congruence Theorem 2.
1 ∠ 3.
Transitive Property of Congruence 3.
1 ∠ 4.
Corresponding Angles Converse
g h 4.

9. Prove the Alternate Interior Angles Theorem
EXAMPLE 3
EXAMPLE 3
Prove the Alternate Interior Angles Theorem
Prove the Alternate Interior Angles Converse
GIVEN :
p q
PROVE :
∠ ∠
STATEMENTS
REASONS 1.
Given 1.
p q 2.
Vertical Angles 2.
3 ∠ 3.
Corresponding Angles 3.
1 ∠ 4.
1 ∠ 4.
Transitive Property

10. Write a paragraph proof
EXAMPLE 3
EXAMPLE 4
Write a paragraph proof
Given: r s and is congruent to
Prove: p q.
STATEMENTS
REASONS
r s 1. 1.
Given 2.
Corresponding Angles 2.
1 ∠ 3.
Given 3.
1 ∠ 4.
Substitution 4.
2 ∠
p q 5 5.
Alternate Interior Angles

11. Given: m || n, n || k Prove: m || k
EXAMPLE 4
Given: m || n, n || k Prove: 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 1 m 2 n 3 k

12. REASONS
STATEMENTS
EXAMPLE 3
EXAMPLE 3

13. Statements Reasons l m, t  l Given 12 Corresponding angles
Given: l m, & t  l,
Proof: t m. t 1 2 l m
Statements
l m, t  l
12
m1=m2
1 is a rt. 
m1=90o
90o=m2
2 is a rt. 
t m
Reasons
Given
Corresponding angles
Def of  s
Def of  lines
Def of rt. 
Substitution