Lesson 2 5 Algebraic Proofs Rigor Use properties

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

Intro to proofs ¢ Workbook pg 61 -62 example 1 ¢ Workbook pg 63 #1 and 3

Notes ¢ Highlight the properties on pg 71 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. Remember! Numbers are equal (=) and figures are congruent ( ).

Example: Justifying single statements ¢ Symmetric Property Distributive Property of Congruence 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 or words) ¢ 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 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