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.

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 paragraphTwo column or formalFlow 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.

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

Justify Each Step When Solving an Equation

Answer: a = –11

–10a = 110 Substitution Property Division Property

a = –11 Substitution Property

A. a = 12

B. a = –37

C. a = –7

D. a = 7

Solve –3(a + 3) + 5(3 – a) = –50.

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

2. d – 5 = 20t 2. Addition Property of Equality

Statements ReasonsProof:

1. Given 1. d = 20t + 5

4. 4. Symmetric Property of Equality

3. 3. Division Property of Equality= t

*Hint* always start with GIVENAlways end with PROVE

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 ReasonsProof:

3. 3. Division Property of Equality

4. 4. Symmetric Property of Equality

1. Given1.

2._____________

2. Multiplication Property of Equality

?2A = (b1 + b2)h

If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture.

5. mA = 90 5. Substitution

Statements ReasonsProof:

4. Substitution4. mA = 2(45)

2. mA = mB 2. Definition of angles

1. Given1. A B; mB = 2mC; mC = 45

3. Transitive Property of Equality

3. mA = 2mC

Statements ReasonsProof:

1. Given1.

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, 18Write out all of the information in the book for

17 & 18That includes:

GivenProve

StatementsReasons