Chapter 2.6 Algebraic Proof.

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Chapter 2.6 Algebraic Proof

Properties you need to know!

State the Property that justifies each statement If 4 + (-5) = -1, Then x + 4 + (-5) = x – 1 If 5 = y, Then y = 5 If 2a = -18, Then a= - 9

Prove that if 2x + 5 = 15, then x = 5 Statements Reasons

Example 1 Statements Reasons Justify Each Step When Solving an Equation Prove that if 2(5 – 3a) – 4(a + 7) = 92, then a = -11 Statements Reasons

Prove that if -3(a+3) + 5(3-a) = -50, then a = 7 Statements Reasons

Postulates

Concept

Example 3 Write a Geometric Proof If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture.

Example 3 1. Given 1. A B; mB = 2mC; mC = 45 2. mA = mB Write a Geometric Proof Statements Reasons Proof: 1. Given 1. A B; mB = 2mC; mC = 45 2. mA = mB 2. Definition of angles 3. Transitive Property of Equality 3. mA = 2mC 4. Substitution 4. mA = 2(45) 5. mA = 90 5. Substitution

Example 3

Example 3 1. Given 1. 2. 2. _______________ ? 3. AB = RS Statements Reasons Proof: 1. Given 1. 2. 2. _______________ ? 3. AB = RS 3. Definition of congruent segments 4. AB = 12 4. Given 5. RS = 12 5. Substitution

Write a two column proof for the conjecture. If CD = EF, and CD=3y – 9, and EF = 15, then y = 8

Example 2 Begin by stating what is given and what you are to prove. Write an Algebraic Proof Begin by stating what is given and what you are to prove.

Try it! Pg. 138 #3A Pg. 139 #7