Name Class Date. Additional Vocabulary Support. Reasoning in Algebra and Geometry

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1 Additional Vocabulary Support Concept List Addition Property of Equality Division Property of Equality Reflexive Property of Equality Subtraction Property of Equality Transitive Property of Equality Distributive Property Multiplication Property of Equality Symmetric Property of Equality Choose the concept from the list above that best represents the item in each box. 1. If a = b, then a + c = b + c 2. If a = b, and c 0, then a = b c c = If a = b, and b = c, then a = c 5. If a = b, then b = a 6. If a = b, then a c = b c 7. 3(12 4) = (3)(12) (3)(4) 8. If a = b, then a c = b c 9. a = 4 6a + 2 = 6( 4) + 2 Prentice Hall Geometry Teaching Resources 41

2 Practice Form G Fill in the reason that justifes each step x + 2x + 12 = 39 Given 2.25x + 12 = 39 a. 2.25x = 27 b. 225x = 2700 c. x = 12 d. 2. Given: m ABC = 80 m ABD + m DBC = m ABC (3x + 3) + (6x + 5) = 80 9x + 8 = 80 9x = 72 x = 8 Angle Addition Postulate a. b. c. 3. Given: KL = 3(PM) 5x = 3(2x 4) 5x = 6x 12 x = 12 x = 12 a. b. c. 4. Given: XY = YZ 8m + 5 = 6m m + 5 = 17 2m = 12 m = 6 a. b. c. Name the property of equality or congruence that justifies going from the first statement to the second statement. 5. XY TZ TZ XY 7. 4n + 6 2n = 9 2n + 6 = (x + 2) = 15 3x + 6 = A B and B C A C Prentice Hall Gold Geometry Teaching Resources 43

3 Practice (continued) Form G 9. Write a two-column proof. Given: QWT and TWX are complementary. Prove: x = 28 1) QWT and TWX are 1) complementary 2) m QWT + m TWX = 90 2) 3) 2x + x + 6 = 90 3) 4) 3x + 6 = 90 4) 5) 3x = 84 5) 6) x = 28 6) 10. Developing Proof Fill in the missing statements or reasons for the two-column proof. Given: E is the midpoint of DF. Prove: DE = 23 1) E is the midpoint of DF. 1) 2) 2) Definition of midpoint 3) 6x + 5 = 8x 1 3) 4) 5 = 2x 1 4) 5) 5) Addition Property of Equality 6) 6) Division Property of Equality 7) DE = 6x + 5 7) Given 8) DE = 6(3) + 5 8) 9) DE = 23 9) 11. Write a two-column proof. Given: m PMN = m RBC Prove: m ABR + m PMN = m ABC Prentice Hall Gold Geometry Teaching Resources 44

4 Practice Form K Algebra Fill in the reason that justifies each step x + 6= 14 3 Given 2. 2(x 12) = 40 Given x + = a. 2x 24 = 40 a. 2x + 18 = 42 b. 2x = 64 b. 2x = 24 c. x = 32 c. x = 12 d. 3. AB = 50 Given AC + CB = AB a. 2x 2 + 4(x + 1) = 50 b. 2x 2 + 4x + 4 = 50 c. 6x + 2 = 50 d. 6x = 48 e. x = 8 f. Name the property of equality or congruence that justifies going from the first statement to the second statement. 4. QR + LM = 20 To start, determine which operation changes QR = 20 LM the first statement to the second statement. 5. ST ST 6. 3x = y 7. 6x 3 y ST ST 3(2x 1) x = 3 Prentice Hall Foundations Geometry Teaching Resources 45

5 Practice (continued) Form K 8. Developing Proof Fill in the missing statements or reasons for the following two-column proof. uuur Given: AB is the bisector of CAD. Prove: x = 9 uuur 1) AB is the bisector of CAD. 2) CAB BAD 3) 1) Given 2)? m CAB m BAD 3) angles have equal measures. 4) 7x + 2 = 5(x + 4) 4)? 5) 7x + 2 = 5x )? 6)? 6)? 7)? 7)? Use the given property to complete each statement. 9. Addition Property of Equality If a = b, then a + 6 = b Symmetric Property of Congruence If LM GH, then GH. 11. Distributive Property 10x 5 = Multiplication Property of Equality If 2 x = 10, then 2x = of Equality If JK = 20 and AB + JK = XY, then = XY. 14. Transitive Property of Congruence If R Z and Z F, then F. Prentice Hall Foundations Geometry Teaching Resources 46

6 Standardized Test Prep Multiple Choice For Exercises 1 6, choose the correct letter. 1. According to the Transitive Property of Equality, if TX 5 XY, and XY 5 YZ, then TX 5 u. TX XY YZ TZ 2. What property is illustrated by the statement, if KL 5 LM, then LM 5 KL? Reflexive Property of Equality Transitive Property of Equality Symmetric Property of Equality Division Property of Equality Use the list of reasons below for Exercises 3 6. Choose the correct reason for each algebraic statement. Subtraction Property of Equality Distributive Property Combine like terms. Division Property of Equality 3(x 1 2) Given 6x ) 9 6x ) 9 6x 5 1 5) 9 x ) 9 Prentice Hall Geometry Teaching Resources 47