3.2/3.4 Postulates, Properties, Definitions and Proofs Warm-up (IN) Learning Objective: to justify statements about geometric figures in 2-column proofs Tell whether the statement is always true, sometimes true, or never true. always never sometimes always

Notes Postulate - Accepted without proof Definition - Biconditional statement - meaning When the hypothesis and conclusion are interchangeable Today is Thursday if and only if tomorrow is Friday. Properties of equality and congruence - Reflexive Property a=a Symmetric Property If a=b, then b=a Transitive Property If a=b and b=c, then a=c Addition Property If a=b, then a+c=b+c

Subtraction Property If a=b, then a-c=b-c Substitution Property If a=b, then a can be substituted for b in an expression Ex 1 – Tell which postulate, property, definition or previous statement makes each statement true Def. of congruent angles Reflexive property Substitution in parts a. and b.

Triangle sum thm Transitive Prop. Subst. and subt. CKC p. 120

EX2 – Write a 2-Column Proof of the theorem: If 2 are supp. to the same, then the are 1 st - Draw a picture!! nd – state what’s given (if) and what you want to prove (then) Given: Prove: 3 rd – make a plan!

4 th – make 2 columns! Statements Reasons # every step! 1. Always start w/given 1. Given 2. Def. Supp. 3. Subst. (step 2) 4. Subt Def. CKC p. 132

HW – p. 121 #4-14,22-28 P #4,10-16 Out – Describe how to write a proof in 2- column format. Summary – Today, I understand… Or I’m still wondering… POW!!