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

Notes ¢ Highlight the properties on pg 71 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 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: supplementary angles Substitution Property Combine like terms Subtraction property of equality Division property of equality

Example 2: Complete the proof 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