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Understanding Angles in Parallel Lines and Transversals

Learn how to identify congruent angles in parallel lines cut by a transversal. Practice finding missing angle measures using postulates and theorems. Solve angle problems and complete proofs with parallel line properties.

jeffreyholmes
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Understanding Angles in Parallel Lines and Transversals

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  1. 3.2 Notes: Angles and Parallel Lines When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent?

  2. In the photo, line t is a transversal of lines a and b, and Ð1 and Ð2 are corresponding angles. Since lines a and b are parallel, there is a special relationship between corresponding angle pairs.

  3. Vocab!

  4. Vocab!

  5. Example 1 Use the diagram below to find the missing angle measure. Tell which postulates (or theorems) you used. a) If m11 = 51, find m15. b) If m11 = 51, find m16.

  6. Example 2 The diagram represents the floor tiles in Michelle’s house. a) If m2 = 125, find m3. b) If m2 = 125, find m4.

  7. You Try! In the figure below , and t is a transversal. If , find the measure of the other angles. m1 _________ m2 _________ m3 _________ m5 _________ m6 _________ m7 _________ m8 _________

  8. Example 4 Use the diagram below to determine the value ofthe variable. a) m5 = (2x – 10)° and m7 = (x + 15)° b) m4 = (4(y – 25))° and m8 = (4y)°

  9. Vocab!

  10. You Try!

  11. Example 5 Complete the proof. Given: a || b Prove: 4  5

  12. Example 6 Complete the proof. Given: a || b Prove: 1  8

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