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LESSON 3.3 NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 143–149 GOAL Prove and use results about parallel lines and transversals and use properties of parallel lines to solve problems VOCABULARY Postulate 15 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Theorem 3.4 If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Theorem 3.5 If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Theorem 3.6 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Theorem 3.7 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. EXAMPLE 1 Using Properties of Parallel Lines Given that m1 32, find each measure. Tell which postulate or theorem you use. a. m2 1 5 b. m3 c. m4 d. m5 4 2 3 Chapter 3 SOLUTION 46 a. m2 32 Corresponding Angles Postulate b. m3 32 Alternate Exterior Angles Theorem c. m4 180 m3 148 Linear Pair Postulate d. m5 32 Vertical Angles Theorem Geometry Practice Workbook with Examples Copyright © McDougal Littell Inc. All rights reserved. LESSON 3.3 CONTINUED NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 143–149 Exercises for Example 1 Find each measure given that m6 67. 1. m7 2. m8 3. m9 4. m10 5. m11 6. m12 6 9 7 8 10 7. m13 EXAMPLE 2 13 11 12 Using Properties of Parallel Lines Use properties of parallel lines to find the value of x. 55 (x 8) SOLUTION x 8 55 x 63 Chapter 3 Alternate Exterior Angles Theorem Add. Exercises for Example 2 Use properties of parallel lines to find the value of x. 8. 9. 140 (2x 4) Copyright © McDougal Littell Inc. All rights reserved. 53 (5x 2) Geometry Practice Workbook with Examples 47 LESSON 3.3 CONTINUED NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 143–149 10. 11. 48 (4x ) 98 (10x 2) 12. 13. (14x 7) (12x) 60 103 14. 15. 135 Chapter 3 (4x 3) (9x 7) 115 48 Geometry Practice Workbook with Examples Copyright © McDougal Littell Inc. All rights reserved.