Properties from Algebra

1. Properties from Algebra 2.2

2. Prosperities of Algebra pg. 37 • Addition Property If a = b and c = d, then a + c = b +d . • Subtraction Property If a = b and c = d, then a-c = b-d. • Multiplication Property If a = b, then ca = cb. • Division Property If a = b, and c ≠ 0, then = • Substitution Property If a = b, then either a or b may be substituted for the other in any equation (or inequality). • Reflexive Property a = a • Symmetric Property If a = b, then b = a • Transitive Property If a = b and b = c, then a = c

3. Properties of Congruence • Reflexive Property: • <D <D • Symmetric Property: • If , then • Transitive Property: • If and , then • If <D <E and <E <F, then <D <F • Distributive Property • a (b + c) = ab + ac

4. Justify Each statement • 1) If AB = CD and BC = BC, then AB + BC = CD + BC. ___________________ • 2) If m< A = ½ m<X and ½ m<X = m<B, then m<A = m<B ___________________ • 3) If point B is in the interior of <XOY, then m< XOB + m<BOY = m< XOY. ____________________ • 4) If 2 + YZ = 8, then YZ = 6. _____________________

5. Geometric Proof Hints • Worksheet

6. Complete Each proof • Given m <1 = m< 3; m <2 = m <4 • Prove m <ABC = m < DEF. Given Addition Property Angle Addition Post. Substitution Property

7. Complete each proof • Given ST = RN; IT = RU • Prove: SI = UN Given ST Segment Addition Postulate RN Substitution Property Given SI = UN Subtraction Property

8. hints • The first statement is almost always the statements that are provided. • Your reasoning should be GIVEN for the first statement. • The last statement is always the what we are trying to prove. • Never use the word “prove” as a reason!

9. Homework • pg. 41-42 WE #1-6