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2.5 Algebraic Proofs

2.5 Algebraic Proofs. Our goal for today is to answer the following guiding question: Why is it important to justify the steps in a proof with reasons?. Proof. Proof argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.

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2.5 Algebraic Proofs

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  1. 2.5 Algebraic Proofs Our goal for today is to answer the following guiding question: • Why is it important to justify the steps in a proof with reasons?

  2. Proof • Proof • argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.

  3. Important • You must give justifications to show that every step is valid

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

  5. Division Property of Equality Example 1: Solving an Equation in Algebra EXAMPLE 1 Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 Given equation +8+8Addition Property of Equality 4m = –4 Simplify. m = –1 Simplify.

  6. Solve the equation . Write a justification for each step. Given equation Multiplication Property of Equality. t = –14 Simplify. EXAMPLE 2

  7. EXAMPLE 3 • What is the temperature in degrees Fahrenheit F when it is 15°C? Solve the equation F = 9/5 C + 32 for F and justify each step.

  8. Given equation Substitution Property of Equality F = 27 + 32 Simplify. F = 59 Simplify. F = 59°

  9. EXAMPLE 42: Solving an Equation in Geometry Write a justification for each step. NO = NM + MO Segment Addition Post. 4x – 4 = 2x + (3x – 9) Substitution Property of Equality 4x – 4 = 5x – 9 Simplify. –4 = x – 9 Subtraction Property of Equality 5 = x Addition Property of Equality

  10.  Add. Post. mABC = mABD + mDBC EXAMPLE 52: Solving an Equation in Geometry Write a justification for each step. 8x°=(3x + 5)°+ (6x – 16)° Subst. Prop. of Equality 8x = 9x – 11 Simplify. –x = –11 Subtr. Prop. of Equality. x = 11 Mult. Prop. of Equality.

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