2-6 Algebraic Proof p. 136

1. 2-6 Algebraic Proofp. 136 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.

2. Proofs A proof is a logical argument in which each statement you make is supported by a statement that is accepted as true. It can be written as: • A paragraph • Two column or formal • Flow chart.

3. Page 136

4. Algebraic Proofs You just saw a table summarizing the properties of real numbers you studied in Algebra. Now you will use these properties in Algebraic Proofs. An algebraic proof is a proof that is made up of a series of algebraic statements.

5. Justify Each Step When Solving an Equation Solve 2(5 – 3a) – 4(a + 7) = 92. Algebraic Steps Properties 2(5 – 3a) – 4(a + 7) = 92 Original equation 10 – 6a – 4a – 28 = 92 Distributive Property –18 – 10a = 92 Substitution Property –18 – 10a + 18 = 92 + 18 Addition Property –10a = 110 Substitution Property Division Property a = –11 Substitution Property Answer:a = –11

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

7. Begin by stating what is given and what you are to prove.

8. Proof: d = 20t + 5 1.Given 1. Statements Reasons 2. d – 5 = 20t 2. Addition Property of Equality = t 3. 3. Division Property of Equality 4. 4. Symmetric Property of Equality *Hint* always start with GIVEN Always end with PROVE

9. If the formula for the area of a trapezoid is , then the height h of the trapezoid is given by . Which of the following statements would complete the proof of this conjecture?

10. Proof: Statements Reasons 1. Given 1. ? 2. _____________ 2. Multiplication Property of Equality 3. 3. Division Property of Equality 4. 4. Symmetric Property of Equality 2A = (b1 + b2)h

11. 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. Statements Reasons mA = 2(45) 4. Substitution 4. 2.mA = mB 2. Definition of angles A B; mB = 2mC; mC = 45 1. Given 1. 5. mA = 90 5. Substitution 3. Transitive Property of Equality 3. mA = 2mC

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

13. 2-6 Assignment Page 139, 2-16 even, 17, 18 Write out all of the information in the book for 17 & 18 That includes: Given Prove Statements Reasons