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**3-4 Proving Lines are Parallel**

Prove that 2 lines are parallel. Use properties of parallel lines to solve problems.

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**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

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**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

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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

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**Identify the Parallel Rays**

B D C

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**3-5 Using Properties of Parallel Lines**

Use properties of parallel lines in problem solving Construct parallel lines

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**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

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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. m1 = m2 3. Right Theorem 4. 1 2 4. Def. of ’s 5. m n 5. Corres. ’s Converse

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