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3.4 – Proving Lines Parallel

3.4 – Proving Lines Parallel. Reasons:. Corresponding Angles Converse – If two lines are cut by a transversal so that the corresponding angles are congruent, then the two lines are parallel

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3.4 – Proving Lines Parallel

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  1. 3.4 – Proving Lines Parallel

  2. Reasons: • Corresponding Angles Converse – If two lines are cut by a transversal so that the corresponding angles are congruent, then the two lines are parallel • Consecutive Interior Angles Converse – If two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the two lines are parallel

  3. More Reasons • Alternate Interior Angles Converse – If two lines are cut by a transversal so that the alternate interior angles are congruent, then the two lines are parallel • Alternate Exterior Angles Converse – If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the two lines are parallel • (use converses when proving parallel lines)

  4. <5 <6, <6 <4 <5 <4 AD | | BC Given Transitive Alternate Interior Angles Converse Given: <5 <6, <6 <4Prove AD | | BC

  5. <1 and <5 are suppl. <4 and < 1 are suppl. <5 <4 j | | k Given Congruent Supplements Theorem Alternate Interior Angles Converse Given: <1 and <5 are supplements, <1 and <4 are supplementsProve: j | | k

  6. Example • What theorem could you use to prove the lines are parallel? Alternate Interior Angles Converse

  7. Assignment • P. 153-154 10-18, 20-28all

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