1. 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

2. 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

3. 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. 6 5 4 3 2 1 Def. of congruent angles Reflexive property Substitution in parts a. and b.

4. 6 5 4 3 2 1 Triangle sum thm Transitive Prop. Subst. and subt. CKC p. 120

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

6. 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. 5. 4. Def. CKC p. 132

7. HW – p. 121 #4-14,22-28 P. 133-134 #4,10-16 Out – Describe how to write a proof in 2- column format. Summary – Today, I understand… Or I’m still wondering… POW!!