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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. Objective. Prove and use theorems about the angles formed by parallel lines and a transversal. Example 1: Using the Corresponding Angles Postulate. Find each angle measure. A. m  ECF. B. m  DCE.

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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

  2. 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 B. mDCE

  4. Check It Out! Example 1 Find mQRS.

  5. Helpful Hint If a transversal is perpendicular to two parallel lines, all eight angles are congruent.

  6. Example 2: Finding Angle Measures Find each angle measure. A. mEDG B. mBDG

  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

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

  9. Lesson Quiz State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures. 1. m1 = 120°, m2 = (60x)° 2. m2 = (75x – 30)°, m3 = (30x + 60)° 3. m3 = (50x + 20)°, m4= (100x – 80)° 4. m3 = (45x + 30)°, m5 = (25x + 10)°

  10. Classwork/Homework • Pg. 158 (1-23 all, 25, 26)

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