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2.5: Algebraic Proof

2.5: Algebraic Proof. Learning Objective SWBAT review properties of equality and use them to write algebraic proofs. Identify properties of equality and congruence. Today is the Big P Day!!!. Take out your homework Take out your whiteboard marker

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2.5: Algebraic Proof

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  1. 2.5: Algebraic Proof Learning Objective • SWBAT review properties of equality and use them to write algebraic proofs. • Identify properties of equality and congruence.

  2. Today is the Big P Day!!! • Take out your homework • Take out your whiteboard marker • If you do not have one, ASK me. Do not borrow a friends (unless they have two)

  3. Math Joke of the Day Why was the math book sad? Because it had too many problems

  4. Whiteboards • Find the measure of segment HJ. • Find the measure of <WXZ.

  5. 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?

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

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

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

  9. 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.

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

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

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

  13. 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

  14.  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.

  15. Remember! Numbers are equal (=) and figures are congruent ().

  16. EXAMPLE 6 Identify the property that justifies each statement. A. QRS  QRS B. m1 = m2 so m2 = m1 C. AB  CD and CD  EF, so AB EF. D. 32° = 32°

  17. EXIT TICKET Please do the following: • Clear your desk. All you need is a pencil and eraser. • You will be given 5 minutes to complete the check for understanding questions. • This is a mini quiz. • NO TALKING • Please remember your name, period, and row #.

  18. 1. Solve the equation. Write a justification for each step. 6r– 3 = –2(r + 1) 2. Identify the property that justifies each statement. • x= y and y = z, so x = z. • DEF  DEF • ABCD, so CDAB. 3. Why is it important to justify the steps in a proof with reasons?

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