• algebraic proof – Made up of algebraic statements

• two-column proof/formal proof – contains statements and reasons in two columns

STEP

1. 3x = 7 – 1/2x

2. 6x = 14 – x

3. 7x = 14

4. x = 2

REASON

1. GIVEN

2. Multiplication Property

3. Addition Property

4. Division Property

It will give you the 1st stepFirst reason is always “given”

Given: 3x = 7 – 1/2x Prove: x = 2

It will give you the last step!

Step

1. 2x + 3 = 11

2. 2x = 8

3. x = 4

Reason

1. Given

2. Subtraction Property

3. Division Property

Write a Geometric Proof

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

5. mA = 90 5. Simplify

Statements ReasonsProof:

4. Substitution4. mA = 2(45)

Write a Geometric Proof

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

A. Reflexive Property of Equality

B. Symmetric Property of Equality

C. Transitive Property of Equality

D. Substitution Property of Equality

Homework

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