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5.3 Congruent Angles Associated With Parallel Lines

5.3 Congruent Angles Associated With Parallel Lines. Objective: After studying this section, you will be able to: apply the parallel postulate, identify the pairs of angles formed by a transversal cutting parallel lines, and apply six theorems about parallel lines.

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5.3 Congruent Angles Associated With Parallel Lines

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  1. 5.3 Congruent Angles Associated With Parallel Lines Objective: After studying this section, you will be able to: apply the parallel postulate, identify the pairs of angles formed by a transversal cutting parallel lines, and apply six theorems about parallel lines.

  2. Postulate: Through a point not on a line there is exactly one parallel to the given line. P

  3. Theorem 37:If two parallel lines are cut by a transversal, each pair of alternate interior angles are congruent. (short form: .) 1 3 2 4

  4. Theorem38:If two parallel lines are cut by a transversal, then any pair of angles formed are either congruent or supplementary. x

  5. Theorem 39:If two parallel lines are cut by a transversal, each pair of alternate exterior angles are congruent. (short form: .) a Given: a ll b 1 Prove: b 8

  6. Theorem 40:If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent. (short form: .) a Given: a ll b 1 Prove: b 5

  7. Theorem 41:If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary. a Given: a ll b Prove: 4 b 6

  8. Theorem 42:If two parallel lines are cut by a transversal each pair of exterior angles on the same side of the transversal are supplementary. a Given: a ll b 2 Prove: b 8

  9. Theorem 43:In a plane, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other. a b Given: a ll b Prove: c

  10. Theorem 44: If two lines are parallel to a third line, they are parallel to each other. (Transitive property of Parallel Lines) a Given: a ll b, b ll c b Prove: a ll c c

  11. If c ll d, find m 1 c 3x + 5 2x + 10 d

  12. Given: F Prove: A D B C E

  13. Given: Prove: 1 g 2 h 3

  14. If a ll b, find m Hint: use the parallel postulate to start a 100 1 C 40 b

  15. Summary If lines are parallel, name the different ways angles are congruent or supplementary. Homework: worksheet

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