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Lesson 5.3

Lesson 5.3. Congruent Angles Associated with Parallel Lines. Most Theorems in this section are converses of what we learned in sec 5-2 In this section we start with parallel lines then state the special pairs of angles.

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Lesson 5.3

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  1. Lesson 5.3 Congruent Angles Associated with Parallel Lines

  2. Most Theorems in this section are converses of what we learned in sec 5-2 • In this section we start with parallel lines then state the special pairs of angles

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

  4. Notice the special tick marks ( ) used to designate parallel lines.

  5. Six Theorems About Parallel Lines

  6. If two parallel lines are cut by a transversal, then • Each pair of alternate interior angles are congruent • Each pair of alternate exterior angles are congruent • Each pair of corresponding angles are congruent • Each pair of interior angles on the same side of the transversal are supplementary • Each pair of exterior angles on the same side of the transversal are supplementary.

  7. Solve Since alt. int. s are , 3x + 5 = 2x + 10 x + 5 = 10 x = 5 3(5) + 5 = 20 Because vertical s are , m1 = 20.

  8. Given ║ lines → alt. int. s  Given Given Addition Property (BC to step 4) SAS (3, 2, 5) CPCTC FA ║ DE A  D FA  DE AB  CD AC  BD ΔFAC  ΔEDB F  E

  9. 5 4 m 3 2 Using the Parallel Postulate, draw m parallel to a. 2 & 3 are congruent (alt. int. s are ) 3 = 40° 4 & 5 are supplementary. 4 = 80° 1 = 40° + 80° = 120°

  10. PAI • PAE • PCA • PSSIS • PSSES • 2P3P • Dual ̸̸ ̸ theorem • Dual ⊥ theorem

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