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Honors Geometry Section 3.4 Proving Lines Parallel

Honors Geometry Section 3.4 Proving Lines Parallel.

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Honors Geometry Section 3.4 Proving Lines Parallel

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  1. Honors Geometry Section 3.4Proving Lines Parallel

  2. With the postulates and theorems of Section 3.3, we are given that lines are parallel and make conclusions about the special angle pairs. In this section, the process is reversed as we look at the converses of the postulates and theorems from Section 3.3.

  3. Postulate 3.4.1 CAP ConverseIf two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

  4. Theorem 3.4.2 SSIAT ConverseIf two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

  5. Theorem 3.4.3 AIAT ConverseIf two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

  6. Theorem 3.4.4 AEAT ConverseIf two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel.

  7. Examples: Determine which lines, if any, will be parallel based on the given information. If lines are parallel, give a reason why (i.e. one of the converses).

  8. Examples: Determine which lines, if any, will be parallel based on the given information. If lines are parallel, give a reason why (i.e. one of the converses).

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