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 + ac

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 1: Justifying single statements
Symmetric Property of Congruence
Distributive Property of Equality

5. Example 2: 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 of equality
Combine like terms
Subtraction property of equality
Division property of equality

6. Example 3: 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 (from picture or words)
Statements about the specific objects go here
Last line is ALWAYS what you are asked to find/prove
Reasons
First reason is always GIVEN
Use definitions, theorems, properties, & formulas to justify each step
NEVER the word “prove” as a reason

8. Back to the work book Turn to page 72
Highlight Segment and Angle Addition Postulates (review from chapter 1)
We will do practice problems 1 and 2 together

9. 2-5 Graded Classwork Assignment
Workbook Pg 73 #4 – 8; pg 74 #3, 4
Honors also do pg 74 #1 & 2
If you don’t finish in class, this is homework
There will not be a Quizizz assignment until we finish 2.6 and 2.7