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LESSON 2.6 NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 109–116 GOAL Use angle congruence properties and prove properties about special pairs of angles VOCABULARY Theorem 2.2 Properties of Angle Congruence Angle congruence is reflexsive, symmetric, and transitive. Theorem 2.3 Right Angle Congruence Theorem All right angles are congruent. Theorem 2.4 Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles) then they are congruent. Theorem 2.5 Congruent Complements Theorem If two angles are complentary to the same angle (or to congruent angles) then the two angles are congruent. Psotulate 12 Linear Pair Postulate If two angles form a linear pair, then they are supplementary. EXAMPLE 1 Chapter 2 Theorem 2.6 Vertical Angles Theorem Vertical angels are congruent. Finding Angles Complete the statement given that mAQG 90. a. mCQE ? b. If mBQG 113, then mEQF ? B C A Q c. mAQG mEQF mBQC ? E G F SOLUTION a. CQE and AQC are vertical angles. By Theorem 2.6, they are con- gruent. By the definition of congruence, mCQE mAQG, so mCQE 90. b. By the Angle Sum Theorem, mBQG mAQG mAQB. Substituting, you get 113 90 mAQB, so mAQB 23 by subtracting. Finally, EQF AQB because they are vertical angles. So, mEQF 23. c. mAQG mAQB mBQC 180. EQF AQB because they are vertical angles. So, mAQG mEQF mBQC 180. Copyright © McDougal Littell Inc. All rights reserved. Geometry Practice Workbook with Examples 37 LESSON 2.6 CONTINUED NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 109–116 Exercises for Example 1 Complete the statement given that mBQD mCQE 90. Explain your reasoning. 1. mAQG ? C D B 2. mCQA ? E Q A F 3. If mCQD 31, then mEQF ? G 4. If mBQG 125, then mCQF ? Chapter 2 5. mAQB mGQF mEQG ? 6. If mEQF 38, then mBQC ? EXAMPLE 2 Finding Angles Find the measure of each numbered angle, given that mDBE 26. C D 2 A 3 1 4 B5 E G F SOLUTION CBD and DBE are complementary. So, m1 90 26 64. ABC and CBE are supplementary. So, m2 180 90 90. ABG and DBE are vertical angles. So, m3 26. GBF and CBD are vertical angles. So, m4 64. EBF and CBE are supplementary. So, m5 180 90 90. 38 Geometry Practice Workbook with Examples Copyright © McDougal Littell Inc. All rights reserved. LESSON 2.6 CONTINUED NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 109–116 Exercises for Example 2 Find the measure of each indicated angle. 7. ACD and ACB D B 54 C A Chapter 2 8. QRT and QRU T 48 R Q U Copyright © McDougal Littell Inc. All rights reserved. Geometry Practice Workbook with Examples 39