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Warm Up Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7

Warm Up Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7. corr. s. alt. int. s. alt. ext. s. same-side int s. Why did the parallel lines not recognize each other?. Because they had never met . Objective.

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Warm Up Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7

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  1. Warm Up Identify each angle pair. 1.1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7 corr. s alt. int. s alt. ext. s same-side int s Why did the parallel lines not recognize each other?

  2. Because they had never met Objective Prove and use theorems about the angles formed by parallel lines and a transversal.

  3. Example 1: Using the Corresponding Angles Postulate Find each angle measure. A. mECF mECF = 70° B. mDCE 5x = 4x + 22 x = 22 mDCE = 5x = 5(22) = 110°

  4. Check It Out! Example 1 Find mQRS. x = 118 mQRS + 118 = 180° Def. of Linear Pair 62° mQRS =

  5. Find the measure of angles 1, 2, 3, and 4.

  6. Check It Out! Example 2 Find mABD. x = 25 mABD = 2(25) + 10 = 60°

  7. Example 3: Music Application Find x and y in the diagram. By the Alternate Interior Angles Theorem, (5x + 4y)° = 55°. By the Corresponding Angles Postulate, (5x + 5y)° = 60°. 5x + 5y = 60 –(5x + 4y = 55) y = 5 Subtract the first equation from the second equation. 5x + 5(5) = 60 x = 7, y = 5

  8. Check It Out! Example 3 Find x and y in the diagram. By the Alternate Exterior Angles Theorem, (25x + 5y)° = 125°. By the Corresponding Angles Postulate, (25x + 4y)° = 120°. X = 4, y = 5

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