+ + 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 If you do not have one, ASK me. Do not borrow a friends (unless they have two) + Math Joke of the Day Why was the math book sad? Because it had too many problems + Whiteboards 1. 1. Find the measure of segment HJ. Find the measure of <WXZ. + + 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. + Important You must give justifications to show that every step is valid + Remember! The Distributive Property states that a(b + c) = ab + ac. Example 1: Solving an Equation in Algebra EXAMPLE 1 Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 +8 +8 Given equation Addition Property of Equality 4m Simplify. = –4 Division Property of Equality m = –1 Simplify. EXAMPLE 2 Solve the equation each step. . Write a justification for Given equation Multiplication Property of Equality. t = –14 Simplify. + 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. Given equation Substitution Property of Equality F = 27 + 32 F = 59 F = 59° Simplify. Simplify. 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 –4 = x – 9 5=x Simplify. Subtraction Property of Equality Addition Property of Equality EXAMPLE 52: Solving an Equation in Geometry Write a justification for each step. mABC = mABD + mDBC Add. Post. 8x° = (3x + 5)° + (6x – 16)° Subst. Prop. of Equality 8x = 9x – 11 –x = –11 x = 11 Simplify. Subtr. Prop. of Equality. Mult. Prop. of Equality. Remember! Numbers are equal (=) and figures are congruent (). EXAMPLE 6 Identify the property that justifies each statement. A. QRS QRS B. m1 = m2 so m2 = m1 C. AB CD and CD EF, so AB EF. D. 32° = 32° + 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 #. + 1. Solve the equation. Write a justification for each step. 6r – 3 = –2(r + 1) 2. Identify the property that justifies each statement. (a) (b) (c) 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?