3-4+Proofs+about+Parallel+Lines

__**Textbook Pages: **__ 150-156

__** Summary: **__ In this section, you will be learning to prove that two lines are parallel. Last section, you learned many theorems that cannot be used unless you know that the two lines are parallel. Finding out if two lines are parallel will follow you in your "geometrical journey" in sections with proofs. Also, knowing if two lines are parallel will help you in the events of architecture, drawing, painting, and landscaping.

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__** Theorems: **__ // If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel //
 * __ ﻿ __ // Theorem 3.8- Alternate Interior Angles Converse //**

//**Theorem 3.9- Consecutive Interior Angles Converse**// //If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel// // m<2+m<1= 180 degrees//

//If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel//
 * //Theorem 3.10- Alternate Exterior Angles Converse//**

__** Postulates: **__ // If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel // **__Examples__** 1. Given: m<1+m<8= 180 degrees Prove: j||k __Statements Reasons__ 1. m<1+m<8=180 degrees 1. Given 2. <1 and <8 are supplementary 2. All angles that equal 180 degrees are supplementary 3. j||k 3. Converse of the Consecutive Interior Angles Theorem
 * // Postulate 16- Corresponding Angles Converse //**

2. Given: <6 is congruent to <8 Prove: j||k __Statements Reasons__ 1. <6 is congruent to <8 1. Given 2. <8 is congruent to <2 2. Alternate interior angles theorem 3. j||k 3. Converse of the Alternate interior angles theorem

3. Given: <3 is congruent to <7 Prove: j||k __Statements Reasons__ 1. <3 is congruent to <7 1. Given 2. <3 is congruent <1 2. Vertical Angles Theorem 3. <1 is congruent to <7 3. Transitive 4. <1 is congruent to <7 4. Converse of the Exterior Angles theorem

4. Given: <3 and <4 are supplementary Prove:j||k __Statements Reasons__ 1.<3 and <4 are supplementary 1. Given 2. <5 and <6 are supplementary 2. Linear Pair 3. <3 is congruent to <5 3. Alternate Exterior Angles theorem 4. j||k 4. Converse of the Alternate Exterior Angles Theorem

**__Practice Problems__** 1. Given: x is the transversal of lines k and j Prove: k||j

2. Given: j is the transversal of lines x and m Prove: x||m

3. Given: x is parallel to m Prove: <A is supplementary to <E

4. Given: <A= 97 degrees <I=97 degrees Prove: k||j