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Proving Lines Parallel

Proving Lines Parallel. Postulate 3-2: Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal and corresponding angles are congruent , then the lines are parallel. Theorem 3-4: Converse of the Alternate Interior Angles Theorem.

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Proving Lines Parallel

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  1. Proving Lines Parallel

  2. Postulate 3-2: Converse of the Corresponding Angles Postulate • If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

  3. Theorem 3-4: Converse of the Alternate Interior Angles Theorem • If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

  4. Postulate 3-6: Converse of the Alternate Exterior Angles Postulate • If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel.

  5. Theorem 3-3: Converse of the Consecutive (Same-Side) Interior Angles Theorem • If two lines are cut by a transversal and consecutive interior angles are supplementary, then the lines are parallel.

  6. Consecutive Exterior Angles • If two lines are cut by a transversal and consecutive exterior angles are supplementary, then the lines are parallel.

  7. 2. 1. 3. 4. Examples: Proving Lines Parallel • Find the value of x which will make lines a and lines b parallel. Answers: 1. 20° 2. 50° 3. 90° 4. 20°

  8. Ways to Prove Two Lines Parallel • Show that corresponding angles are equal. • Show that alternative interior angles are equal. • Show that consecutive interior angles are supplementary. • Show that consecutive exterior angles are supplementary. • In a plane, show that the lines are perpendicular to the same line.

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