2-6 Algebraic Proof p. 136 You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties.

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Presentation transcript:

2-6 Algebraic Proof p. 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.

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.

Page 136

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.

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

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

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

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

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

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

3. Transitive Property of Equality 3. mA = 2mC 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 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

3. Definition of congruent segments 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 Transitive Property of Equality

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