1. Lesson 2-5: Algebraic Proofs
Rigor – Use properties of equality,
postulates, and definitions to justify
steps in a proof.
Relevance – logical thinking and
proofs

2. Notes Highlight the properties on pg71 of the work book.
Add the distributive property of equality to the list
Distributive Property of Equality:
a(b + c) = ab + bc

3. Properties of Congruence
You learned in Chapter 1 that segments with equal lengths are congruent and that angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.
Numbers are equal (=) and figures are congruent ().
Remember!

4. Example: Justifying single statements
Symmetric Property of Congruence
Distributive Property of Equality

5. Example: Justify each step used to solve for x.
Think, what relationship do you see in the diagram?
Definition of linear pair
Linear Pair Theorem
Substitution Property
Combine like terms
Subtraction property of equality
Division property of equality

6. Example 2: Justify each step
Definition of a bisector
Substitution Property of equality
Subtraction property of equality
Division property of equality

7. Two – Column Proofs Format
Statements
First statement is always given info
This side is for work
No skipping steps
Last line is ALWAYS what you are asked to find/prove
Reasons
First reason is always GIVEN (from picture, words, definitions)
Definitions, theorems, properties, formulas go here
The last reason is NEVER “prove”

8. Back to the work book Turn to page 72
We will do practice problems 1 and 2 together

9. 2-5 Assignment from the Work Book
Pg 73 #4 – 8
Honors also do pg 74 #1 & 2
Due Tuesday (Periods 2, 4, & 6)
Due Wednesday (Periods 1, 5, & 7)
Quiz the week of 10/17 will cover up to this point (2-2, 2-4, & 2-5)