1. 2-6 Algebraic Proof 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.

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.
STATEMENTS REASONS
2(5 – 3a) – 4(a + 7) = 92 Given
10 – 6a – 4a – 28 = 92 Distributive Property
– 10a - 18 = 92 Substitution Property
-10a = 110 Addition Property
a = -11
Division Property

6. Justify Each Step When Solving an Equation
Solve -3(a + 3) + 5(3 - a) = -50.
STATEMENTS REASONS
-3(a + 3) + 5(3 - a) = -50 Given
-3a – – 5a = -50 Distributive Property
-8a + 6 = Substitution Property
-8a = Subtraction Property
a = Division Property

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

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

9. 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

10. 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