1. 2.5 Algebraic Proof
Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations.

2. Guiding Question: Why can we solve algebra problems the way we do?
Objectives: IWBAT review properties of equality and use them to write algebraic proofs. Identify properties of equality and congruence. Proof: An argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.

3. 2.5 Properties of Equality
The Distributive Property states that
a(b + c) = ab + ac.
Remember!

4. 2.5 Properties of Congruence

5. What’s the Difference? Helpful Hint A B
AB represents the length AB, so you can think of AB as a variable representing a number.
Helpful Hint

6. Geometric objects can be congruent to each other.
Congruence
Equality
Geometric objects can be congruent to each other.
Measurements can be equal to each other.
Numbers are equal (=) and figures are congruent ().
Remember!

7. Guiding Question: Why can we solve algebra problems the way we do?
Statement
Reason

8. Guiding Question: Why can we solve algebra problems the way we do?

9. Guiding Question: Why can we solve algebra problems the way we do?
Write a justification for each step. NO = NM + MO Segment Addition Post. 4x – 4 = 2x + (3x – 9) Substitution Property of Equality 4x – 4 = 5x – 9 Simplify. –4 = x – 9 Subtraction Property of Equality 5 = x Addition Property of Equality

10. Guiding Question: Why can we solve algebra problems the way we do?
Assignment: Algebraic Proof WS