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Drill: Monday, 11/7 Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7

Drill: Monday, 11/7 Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7 OBJ: Prove theorems about the angles formed by parallel lines and a transversal. Angles Formed by Parallel Lines and Transversals. 3-2. Warm Up. Lesson Presentation. Lesson Quiz.

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Drill: Monday, 11/7 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. Drill: Monday, 11/7 Identify each angle pair. 1.1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7 OBJ: Prove theorems about the angles formed by parallel lines and a transversal.

  2. Angles Formed by Parallel Lines and Transversals 3-2 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

  3. Example 1: Using the Corresponding Angles Postulate Find each angle measure. A. mECF x = 70 Corr. s Post. mECF = 70° B. mDCE 5x = 4x + 22 Corr. s Post. x = 22 Subtract 4x from both sides. mDCE = 5x = 5(22) Substitute 22 for x. = 110°

  4. Check It Out! Example 1 Find mQRS. x = 118 Corr. s Post. mQRS + x = 180° Def. of Linear Pair Subtract x from both sides. mQRS = 180° – x = 180° – 118° Substitute 118° for x. = 62°

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

  6. Remember that postulates are statements that are accepted without proof. Since the Corresponding Angles Postulate is given as a postulate, it can be used to prove the next three theorems.

  7. Example 2: Finding Angle Measures Find each angle measure. A. mEDG mEDG = 75° Alt. Ext. s Thm. B. mBDG x – 30° = 75° Alt. Ext. s Thm. x = 105 Add 30 to both sides. mBDG = 105°

  8. Check It Out! Example 2 Find mABD. 2x + 10° = 3x – 15° Alt. Int. s Thm. Subtract 2x and add 15 to both sides. x = 25 mABD = 2(25) + 10 = 60° Substitute 25 for x.

  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)° Alt. Ext. s Thm.; m2 = 120° Corr. s Post.; m2 = 120°, m3 = 120° 3. m3 = (50x + 20)°, m4= (100x – 80)° 4. m3 = (45x + 30)°, m5 = (25x + 10)° Alt. Int. s Thm.; m3 = 120°, m4 =120° Same-Side Int. s Thm.; m3 = 120°, m5 =60°

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