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

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!

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 of linear pair Linear Pair Theorem Substitution Property Combine like terms Subtraction property of equality Division property of equality

Example 2: Justify each step     Definition of a bisector   Substitution Property of equality   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 (from picture, words, definitions) Definitions, theorems, properties, formulas go here The last reason is NEVER “prove”

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

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)