Lesson 2-5: Algebraic Proofs

Rigor – Use properties of equality,

postulates, and definitions to justify

steps in a proof.

Relevance – logical thinking and

proofs

Notes

Highlight the properties on pg71 of the corebook

Add the distributive property of equality to the list

Distributive Property of Equality:

a(b + c) = ab + bc

Example: Justifying single statements

Symmetric Property of Congruence

Distributive Property of Equality

Example: Justify each step used to solve for x.

Think, what relationship do you see in the diagram?

Definition: supplementary angles

Substitution Property

Combine like terms

Subtraction property of equality Division property of equality

Example 2: Complete the proof

2 75x x m RAB m BAN

75x 75x

Definition of a bisector

Substitution Property

Subtraction property of equality

Division property of equality

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 info (picture, words, definitions)

Definitions, theorems, properties, formulas go here

The last reason is NEVER “prove”

Back to the core book

Turn to page 72

We will do practice problems 1 and 2 together

2-5 Classwork from the Core Book

Pg 73 #4 – 8

Be ready to move on in 15 minutes

You will be assigned 2-5 homework next week