2. Vocabulary algebraic proof – Made up of algebraic statements two-column proof/formal proof – contains statements and reasons in two columns

3. Concept

4. Proof STEP 1. 3x = 7 – 1/2x 2. 6x = 14 – x 3. 7x = 14 4. x = 2 REASON 1. GIVEN 2. Multiplication Property 3. Addition Property 4. Division Property It will give you the 1 st step First reason is always “given” Given: 3x = 7 – 1/2x Prove: x = 2 It will give you the last step!

5. TOO: 3 Steps Step 1. 2x + 3 = 11 2. 2x = 8 3. x = 4 Reason 1. Given 2. Subtraction Property 3. Division Property

6. 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.

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

8. Example 3

9. StatementsReasons Proof: 1. Given 1. 2.2. _______________ ? 3. AB = RS3. Definition of congruent segments 4. AB = 124. Given 5. RS = 125. Substitution

10. Example 3 A. Reflexive Property of Equality B. Symmetric Property of Equality C.Transitive Property of Equality D. Substitution Property of Equality

11. Homework Page 139 (9-18, 23-26)