3 4 PROVING LINES ARE PARALLEL Prove that








- Slides: 8

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

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 1 Prove: p q 3 2 Statements 1. 1 2 Reasons 2. 1 3 1. Given 2. Vert. ’s Theorem 3. 2 3 4. p q 3. Trans. POC 4. Corres. ’s Converse 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 Given: Angles 4 and 5 are supplementary. Prove: p and q are parallel Statements 6 4 p 5 q Reasons 1. 4 and 5 are supplementary. 1. Given 2. 5 and 6 are supplementary. 2. Linear Pair Postulate 3. 4 6 4. p q 3. Supplements Theorem 4. AIA Converse

Identify the Parallel Rays E A F B C D

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 p Given: 1 Prove: 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: 1 2 p Prove: 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