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Section 3-4

This post discusses the converse of the corresponding angles postulate and alternate interior angles theorem to prove the parallelism of lines when certain angle conditions are met.

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Section 3-4

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  1. Section 3-4 Proving Lines are Parallel

  2. Converse of Corresponding Angles postulate • If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

  3. j 1 k 2 j║k therefore

  4. Converse of Alternate interior Angles theorem • If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

  5. j 3 k 4 If , then j║k.

  6. Converse of consecutive interior Angles theorem • If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

  7. j 5 k 6 If , then j║k.

  8. Converse of Alternate exterior Angles theorem • If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

  9. j 7 k 8 If , then j║k.

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