1. UNIT 01 – LESSON 11 – ALGEBRAIC PROOFS ESSENTIAL QUESTION How can algebraic properties help you solve an equation? SCHOLARS WILL… Use algebra to write two-column proofs Use properties of equality to write geometric proofs.

2. WHAT IS AN ALGEBRAIC PROOF? An algebraic proof is a proof is a proof that is made up of a series of algebraic statements. The properties of equality provide justification for many statements in algebraic proofs.

3. ALGEBRAIC PROPERTIES OF EQUALITY (CARD #12)

4. HOW DO YOU JUSTIFY EACH STEP WHEN SOLVING EQUATIONS? Algebraic StepsProperties 2(5 – 3a) – 4(a + 7)=92Original equation 10 – 6a – 4a – 28=92Distributive Property –18 – 10a=92Substitution Property –18 – 10a + 18 =92 + 18Addition Property –10a=110 Substitution Property a=–11 Substitution Property

5. HOW DO YOU JUSTIFY EACH STEP WHEN SOLVING EQUATIONS? Solve –3(a + 3) + 5(3 – a) = –50. Justify each step.

6. HOW DO YOU WRITE AN ALGEBRAIC PROOF?

7. Begin by stating what is given and what you are to prove. 2. d – 5 = 20t2. Addition Property of Equality StatementsReasons Proof: 1. Given 1. d = 20t + 5 4.4. Symmetric Property of Equality 3.3. Division Property of Equality = t

8. HOW DO YOU 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.

9. 5. m  A = 90 5. Substitution StatementsReasons Proof: 4. Substitution 4. m  A = 2(45) 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

10. TRY ON YOUR OWN: If the formula for the area of a trapezoid is, then the height h of the trapezoid is given by.