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Name Class 2-5 Date Practice Form G Reasoning in Algebra and Geometry Fill in the reason that justifies each step. 1. 0.25x 1 2x 1 12 5 39 Given Combine like terms, using the a. 9 Distributive Property. 2.25x 1 12 5 39 2.25x 5 27 b. 9 Subtraction Property of Equality 225x 5 2700 c. 9 Multiplication Property of Equality d. 9 Division Property of Equality x 5 12 2. Given: m/ABC 5 80 m/ABD 1 m/DBC 5 m/ABC Angle Addition Postulate (3x 1 3) 1 (6x 1 5) 5 80 Substitution Property A Combine like terms, using the Associative and Distributive Properties. 9x 1 8 5 80 a. 9 Subtraction Property of Equality B 9x 5 72 b. 9 Division Property of Equality x58 c. 9 3. Given: KL 5 3(PM) 5x 5 3(2x 2 4) (3x 3) (6x 5) C 5x K Substitution Property Distributive Property a. 9 Subtraction Property of Equality 2x 5 212 b. 9 Multiplication Property of Equality x 5 12 c. 9 L 2x 4 5x 5 6x 2 12 P M 4. Given: XY 5 YZ 6m 17 8m 5 X Y 8m 1 5 5 6m 1 17 Substitution Property 2m 1 5 5 17 a. 9 Subtraction Property of Equality 2m 5 12 b. 9 Subtraction Property of Equality c. 9 Division Property of Equality m56 D Name the property of equality or congruence that justifies going from the first statement to the second statement. 5. XY > TZ 6. 3(x 1 2) 5 15 TZ > XY 3x 1 6 5 15 Symmetric Property of Congruence Distributive Property 8. /A > /B and /B > /C 7. 4n 1 6 2 2n 5 9 /A > /C 2n 1 6 5 9 Combine like terms, using the Associative and Distributive Properties. Transitive Property of Congruence Prentice Hall Gold Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 43 Z Name Class 2-5 Date Practice (continued) Form G Reasoning in Algebra and Geometry 9. Write a two-column proof. Given: /QWT and /TWX are complementary. Q Prove: x 5 28 T (2x) Statements Reasons (x 6) 1) /QWT and /TWX are 1) 9 Given X W complementary 2) m/QWT 1 m/TWX 5 90 2) 9 Definition of complementary angles 3) 2x 1 x 1 6 5 90 3) 9 Substitution Property 4) 3x 1 6 5 90 4) 9 Combine like terms. 5) 3x 5 84 5) 9 Subtraction Property of Equality 6) x 5 28 6) 9 Division Property of Equality 10. Developing Proof Fill in the missing statements or reasons 6x 5 for the two-column proof. D 8x 1 E F Given: E is the midpoint of DF . Prove: DE 5 23 Statements Reasons 1) E is the midpoint of DF . 1) 9 Given 2) 9 DE 5 EF 2) Definition of midpoint 3) 6x 1 5 5 8x 2 1 3) 9 Substitution Property 4) 5 5 2x 2 1 4) 9 Subtraction Property of Equality 5) Addition Property of Equality 5) 9 6 5 2x 6) 9 3 5 x 7) DE 5 6x 1 5 6) Division Property of Equality 8) DE 5 6(3) 1 5 9) DE 5 23 8) 9 Substitution Property 7) Given 9) 9 Simplify. 11. Write a two-column proof. A Given: m/PMN 5 m/RBC M R Prove: m/ABR 1 m/PMN 5 m/ABC B Reasons Statements P C 1) mlPMN 5 mlRBC 1) Given 2) mlABR 1 mlRBC 5 mlABC 2) Angle Addition Postulate 3) mlABR 1 mlPMN 5 mlABC 3) Substitution Property Prentice Hall Gold Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 44 N