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Lesson 2.7 , For use with pages 124-131

=. 1. If m 1 = 90º and m 2 = 90º , then m 1 = m 2. 3. If FG RS, then FG = RS. 2. If AB BC , then ABC is a right angle. ┴. Lesson 2.7 , For use with pages 124-131. Give a reason for each statement. Objective: TSWBAT write two-column proofs involving angles.

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Lesson 2.7 , For use with pages 124-131

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  1. = 1.Ifm 1 = 90º andm 2 = 90º,thenm 1 = m 2. 3.IfFG RS,thenFG = RS 2.IfAB BC , thenABC is a right angle. ┴ Lesson 2.7, For use with pages 124-131 Give a reason for each statement.

  2. Objective: TSWBAT write two-column proofs involving angles. • Homework: - Pg 127 #1-33 eoo

  3. Write a proof. ABBC, DCBC GIVEN: BC PROVE: REASONS STATEMENT 1. 1. ABBC, DCBC Given 2. 2. Definition of perpendicular lines Band Care right angles. 3. BC 3. Right Angles Congruence Theorem EXAMPLE 1 Use right angle congruence

  4. Prove that two angles supplementary to the same angle are congruent. GIVEN: 1 and 2 are supplements. 3 and 2 are supplements. • 3 PROVE: EXAMPLE 2 Prove a case of Congruent Supplements Theorem

  5. REASONS STATEMENT 1. 1. 1 and 2 are supplements. Given 3 and 2 are supplements. 2. 2. m1+m2= 180° Definition of supplementary angles m3+m2= 180° 3. m 3 +m 2 3. m 1 +m 2 = Substitution Property of Equality 4. m1=m3 4. Subtraction Property of Equality 5. • 3 5. Definition of congruent angles EXAMPLE 2 Prove a case of Congruent Supplements Theorem

  6. ANSWER 2 Steps for Examples 1 and 2 GUIDED PRACTICE 1. How many steps do you save in the proof in Example 1 by using the Right Angles Congruence Theorem? 2. Draw a diagram and write GIVEN and PROVE statements for a proof of each case of the Congruent Complements Theorem.

  7. ANSWER Write a proof. Given: 1 and 3 are complements; 3 and 5 are complements. Prove:∠ 1 5 for Examples 1 and 2 GUIDED PRACTICE

  8. Statements (Reasons) 1.1 and 3 are complements; 3 and 5 are complements. (Given) 2.∠ 1 5 Congruent Complements Theorem. for Examples 1 and 2 GUIDED PRACTICE

  9. Prove vertical angles are congruent. 5 and 7 are vertical angles. GIVEN: ∠ 5 ∠ 7 PROVE: EXAMPLE 3 Prove the Vertical Angles Congruence Theorem

  10. REASONS STATEMENT 6 and 7 are a linear pair. 5 and 7 are vertical angles. 6 and 7 are supplementary. 5 and 6 are a linear pair. 5 and 6 are supplementary. 1. 1. Given ∠ 5 ∠ 7 2. 2. Definition of linear pair, as shown in the diagram 3. 3. Linear Pair Postulate 4. 4. Congruent Supplements Theorem EXAMPLE 3 Prove the Vertical Angles Congruence Theorem

  11. In Exercises 3–5, use the diagram. 3. If m 1 = 112°, find m 2, m 3, and m 4. ANSWER m 2 = 68° m 3 = 112° m 4 = 68° for Example 3 GUIDED PRACTICE

  12. 5. If m 4 = 71°, find m 1, m 2, and m 3. 4. If m 2 = 67°, find m 1, m 3, and m 4. ANSWER ANSWER m 1 = 113° m 3 = 113° m 4 = 67° m 1 = 109° m 2 = 71° m 3 = 109° for Example 3 GUIDED PRACTICE

  13. ANSWER Congruent Supplements Theorem for Example 3 GUIDED PRACTICE 6. Which previously proven theorem is used in Example 3 as a reason?

  14. Because TPQand QPRform a linear pair, the sum of their measures is 180. ANSWER The correct answer is B. EXAMPLE 4 Standardized Test Practice SOLUTION

  15. Because TPQand QPRform a linear pair, the sum of their measures is 180°. The correct answer is B. for Example 4 GUIDED PRACTICE Use the diagram in Example 4. 7. Solve for x. SOLUTION 32 + (3x +1) = 180 Original equation 32 + 3x +1 = 180 Distributive property of equality 3x = 147 Subtract 33 from each side x = 49 Divide each side by 3

  16. 8. Find m TPS. m TPS = (3x + 1)° m TPS = (147 +1)° m TPS = 148° m TPS = (3 49 +1)° for Example 4 GUIDED PRACTICE Use the diagram in Example 4. SOLUTION Substitute the value x = 49

  17. ClosureProperties of Congruence

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