1. Bell Ringer

2. Then/Now You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties of equality to write geometric proofs.

3. Vocabulary algebraic proof two-column proof formal proof

4. Concept

14. Example 1 Justify Each Step When Solving an Equation Solve 2(5 – 3a) – 4(a + 7) = 92. 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

15. Example 1 Justify Each Step When Solving an Equation Answer: a = –11 –10a=110Substitution Property Division Property a=–11Substitution Property

16. Example 1 A.a = 12 B.a = –37 C.a = –7 D.a = 7 Solve –3(a + 3) + 5(3 – a) = –50.

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

18. Example 2 Write an Algebraic Proof 2. d – 5 = 20t2. Subtraction Property of Equality StatementsReasons Proof: 1. Given 1. d = 20t + 5 4.4. Symmetric Property of Equality 3.3. Division Property of Equality = t