1. Geometry 2.5 Big Idea: Reason Using Properties from Algebra

2. Algebraic Properties of Equality Addition Property If a = b, then a + c = b + c If a = b, then a + c = b + c Subtraction Property Subtraction Property If a = b, then a - c = b – c If a = b, then a - c = b – c (This is what we do when we solve equations.)

3. Multiplication Property If a = b, then ac = bc If a = b, then ac = bc Division Property If a = b and c ≠ 0, If a = b and c ≠ 0, then a = b then a = b c c c c

4. Substitution Property If a = b, then ‘ a ’ can be substituted for ‘ b ’ in any equation. (and vice-versa) If a = b, then ‘ a ’ can be substituted for ‘ b ’ in any equation. (and vice-versa) Distributive Property a(b + c) = ab + ac a(b + c) = ab + ac

5. Reflexive Property of Equality Real Numbers: a = a Segment Length: AB = AB Angle Measure: m A = m A

6. Symmetric Property of Equality Real Numbers: if a = b, then b = a Segment Length: if AB = CD, then CD = AB then CD = AB Angle Measure: if m A = m B, then m B = m A, then m B = m A,

7. Transitive Property of Equality Real Numbers: if a = b and b = c, then a = c then a = c Segment Length: if AB = CD and CD = EF, then AB = EF CD = EF, then AB = EF Angle Measure: if m A = m B and m B = m C, then m A=m C

8. Example: Solve. Write a reason for each step. Given Add. Prop. Of Eq. Sub. Prop. Of Eq. Div. Prop. Of Eq.

9. Example: Solve. Write a reason for each step.