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2-5 Algebraic Proof Vocabulary Proof: an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. 3 Aspects of Proof: 1. Starts with a given fact. 2. Is logical and organized. 3. Every step is justified (has a reason). Example 1: Solving an Equation in Algebra Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 +8 +8 4m = –4 Given equation Addition Property of Equality Simplify Division Property of Equality m = –1 Simplify Example 2: Problem-Solving Application What is the temperature in degrees Fahrenheit F when it is 15°C? Solve the equation F =9 C + 32 5 for F and justify each step. Given equation Substitution Property of Equality F = 27 + 32 F = 59 F = 59° Simplify. Simplify. Example 3: Solving an Equation in Geometry Solve for x. Write a justification for each step. NO = NM + MO Segment Addition Post. 4x – 4 = 2x + (3x – 9) Substitution Prop. of Equality 4x – 4 = 5x – 9 –4 = x – 9 5=x Simplify Subtraction Prop. of Equality Addition Prop. of Equality Example 4: Identifying Property of Equality and Congruence Identify the property that justifies each statement. A. QRS QRS Reflex. Prop. of . B. m1 = m2 so m2 = m1 Symm. Prop. of = C. AB CD and CD EF, so AB EF. Trans. Prop of D. 32° = 32°Reflex. Prop. of =