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

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

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

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

Identify the Parallel Rays B D C

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

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

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