1. 2.5 Reasoning and Algebra

2. Addition Property If A = B then A + C = B + C

3. Subtraction Property If A = B then A – C = B - C

4. Multiplication Property If A = B then AC = BC

5. Division Property If A = B and C is not 0 then A/C = B/C Why cant C = 0?

6. Substitution Property If A = B then A can be substituted for B in any equation

7. Distributive property A(B + C) = AB + AC

8. Reflexive Property For real numbers: A= A For Segments AB = AB For angles m<A = m<A

9. Symmetric Property For real numbers: if A = B then B = A For segments: if AB = CD then CD = AB For angles: If m<A = m<B then m<B = m<A

10. Transitive Property For real numbers: If A = B and B = C then A = C For Segments: if AB = BC and BC = CD then AB = CD For angles: if m<A = m<B and m<C = m<D then m<A = m<C

11. Proofs This is an explanation of what you are doing to solve a problem or prove a theory You use the rules you know to do this

12. 2 Column Proof

13. Proofs

16. 2x + 15 = 3x + 10 15 = x + 10 5 = x X = 5 Given Subtraction Symmetric

17. 5X – 9 = 3X + 1 2X – 9 = 1 2X = 10 X = 5 Given Subtraction Addition Division

18. 2(X – 5) = 3X + ½ 2X – 10 = 3X + ½ -10 = X + ½ -20 = 2X + 1 -21 = 2X -10.5 = X X = -10.5 Given Distributive Subtraction Multiplication Subtraction Division Symmetric