1. 3-4 Proving Lines are Parallel
Prove that 2 lines are parallel.
Use properties of parallel lines to solve problems.

2. Corresponding Angles Converse Postulate
If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. 1 2

3. Proving AIA Converse Given: 1  2 Prove: p q 1. 1  2 1. Given
Theorem 3.8 (AIA Converse): If 2 lines are cut by a transversal so that AIA are congruent then the lines are parallel.
Proving AIA Converse
Given: 1  2
Prove: p q 3 p 1 2 q
Statements
Reasons
1. 1  2
1. Given
2. Vert. ’s Theorem
2. 1  3
3. Trans. POC
3. 2  3
4. Corres. ’s Converse
4. p q

4. Theorem 3.9 (CIA Converse): If 2 lines are cut by a transversal so that CIA are supplementary then the lines are parallel.
Proving CIA Converse p
Given: Angles 4 and 5 are supplementary.
Prove: p and q are parallel 6 5 4 q
Reasons
Statements
1. 4 and 5 are supplementary.
1. Given
2. 5 and 6 are supplementary.
Linear Pair Postulate
3. 4  6
3.  Supplements Theorem
4. p q
4. AIA Converse

5. Identify the Parallel RaysB D C

6. 3-5 Using Properties of Parallel Lines
Use properties of parallel lines in problem solving
Construct parallel lines

7. Theorem 3.11: If 2 lines are parallel to the same line, they are parallel to each other
Given:
Prove: 1 q r 2 3
1. p q, q r
1. Given
2. 1  2
2. Corres. ’s Post.
3. 2  3
3. Corres. ’s Post.
4. 1  3
4. Trans. POC
5. p r
5. Corres. ’s Converse

8. Theorem 3.12: If 2 lines in the same plane are perpendicular to the same line, they are parallel to each other
Given:
Prove: 1 2 p m n
1. m  p, n  p
1. Given
2. 1 & 2 are right angles.
2. Def. of  lines
3. m1 = m2
3. Right   Theorem
4. 1 2
4. Def. of  ’s
5. m n
5. Corres. ’s Converse