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 + ac

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

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

Example 3: 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 (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

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

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