11/22/2016 Geometry 1 Section 2.4: Reasoning with Properties from Algebra

11/22/2016 Geometry 2 Algebraic Properties of Equality Let a, b, and c be real numbers Addition Property –If a = b, then a + c = b + c Subtraction Property –If a = b, then a - c = b – c Multiplication Property –If a = b, then ac = bc Division Property –If a = b and c ≠ 0, then a  c = b  c

11/22/2016 Geometry 3 Reflexive Property –For any real number a, a = a Symmetric Property –If a = b, then b = a Transitive Property –If a = b and b = c, then a = c Substitution Property –If a = b, then a can be substituted for b in any equation or expression

11/22/2016 Geometry 4 Example 1: Writing Reasons Solve 3x + 12 = 8x -18 and write a reason for each step – 3x + 12 = 8x -18 (Given) –12 = 5x -18 (Subt. Prop of =) –30 = 5x (Addition Prop of =) –6 = x (Division Prop. of =)

11/22/2016 Geometry 5 Properties of Equality Reflexive –Segment Length For any segment AB, AB = AB –Angle Measure For any angle A, m  A = m  A

11/22/2016 Geometry 6 Symmetric –Segment Length If AB = CD, then CD = AB –Angle Measure If m  A = m  B, then m  B = m  A Transitive –Segment Length If AB = CD and CD = EF, then AB = EF –Angle Measure If m  A = m  B and m  B = m  C, then m  A = m  C

11/22/2016 Geometry 7 Example 2: Using Prop. Of Length AC = BD. Verify that AB = CD. StatementsReasons AC = BDGiven BC = BCRefl. Prop of = AC – BC = BD – BC- Prop of = AB + BC = AC; BC + CD = BDSegment Add. Postulate AB = AC – BC; CD = BD – BCSubtraction prop of = AB = CDSubs. Prop of = A BCD