3 2 Angles Formed by Parallel Lines and

3 -2 Angles Formed by Parallel Lines and Transversals Warm Up Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7 Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Objective Prove and use theorems about the angles formed by parallel lines and a transversal. Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Example 1: Using the Corresponding Angles Postulate Find each angle measure. A. m ECF B. m DCE Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Check It Out! Example 1 Find m QRS. Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Helpful Hint If a transversal is perpendicular to two parallel lines, all eight angles are congruent. Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Example 2: Finding Angle Measures Find each angle measure. A. m EDG B. m BDG Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Example 3: Music Application Find x and y in the diagram. By the Alternate Interior Angles Theorem, (5 x + 4 y)° = 55°. By the Corresponding Angles Postulate, (5 x + 5 y)° = 60°. 5 x + 5 y = 60 5 x + 4 y = 55 Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Check It Out! Example 3 Find the measures of the acute angles in the diagram. By the Alternate Exterior Angles Theorem, (25 x + 5 y)° = 125°. By the Corresponding Angles Postulate, (25 x + 4 y)° = 120°. Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Lesson Quiz State 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 = (60 x)° 2. m 2 = (75 x – 30)°, m 3 = (30 x + 60)° 3. m 3 = (50 x + 20)°, m 4= (100 x – 80)° 4. m 3 = (45 x + 30)°, m 5 = (25 x + 10)° Holt Mc. Dougal Geometry

3 -2 Angles Formed by Parallel Lines and Transversals Classwork/Homework • Pg. 158 (1 -23 all, 25, 26) Holt Mc. Dougal Geometry