1. Warm Up Solve each equation. 1. 2. 3. 4t – 7 = 8t + 3 4. 5. 2(y – 5) – 20 = 0 x = 7 r = 12.2 or - 5.2 n = 17 y = 15

2. Proof! Vocabulary Today we will review properties of equality from algebra and use them to write “algebraic” proofs. A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid.

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4. The Distributive Property states that a(b + c) = ab + ac. Remember!

5. Solve the equation 4m – 8 = 12. Write the justification for each step. Given equation Addition Property of Equality Simplify Division Property of Equality

6. Given equation Multiplication Property of Equality Simplify Subtraction Property of Equality Solve the equation. Write the justification for each step. Simplify Division Property of Equality

7. Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry. A B AB represents the length, so you can think of AB as a variable representing a number. Helpful Hint

8. Write a justification for each step. NO = NM + MO 4x – 4 = 2x + (3x – 9) Substitution Property of Equality Segment Addition Post. 4x – 4 = 5x – 9 –4 = x – 9 5 = x Addition Property of Equality Subtraction Property of Equality Simplify.

9. Write a justification for each step. 8x° = (3x + 5)° + (6x – 16)° Subst. Prop. of = x = 11 8x = 9x – 11 –x = –11 Simplify. Subtr. Prop. of Equality. Mult. Prop. of Equality.

10. Key Idea You learned in Chapter 1 that segments with equal lengths are congruent and that angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality each have corresponding properties of congruence.

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12. Remember ! Identify the property that justifies each statement.

13. Lesson Quiz Solve the equation and write justification for each step. 6r – 3 = -2(r + 1) Given 6r – 3 = -2r - 2 Distributive Property 8r – 3 = -2 Addition Property of Equality 8r = 1 Addition Property of Equality Division Property of Equality

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