2.4 Algebraic Reasoning

What We Will Learn Use algebraic properties of equality to justify steps in solving Use distributive property to justify steps in solving Use properties of equality involving segment lengths and angle measures

Needed Vocab Addition Prop: If a = b, then a+c = b+c Subtraction Prop: a-c = b-c Multiplication prop: a⋅c = b⋅c Division prop: 𝑎 𝑐 = 𝑏 𝑐 Substitution prop: If a = b, then a can be substituted for b (or b for a) in any equation or expression Distributive prop: a(b+c) = ab + ac Reflexive Prop of Equality: a = a Symmetric Prop of Equality: If a = b, then b = a Transitive Prop of Equality: If AB = CD and CD = EF, then AB = EF.

Ex. 1 Justifying Steps Start of proofs Solve and justify Statement +11 +11 6x = -24 6𝑥 6 = −24 6 x = -4 Reason Given Addition Prop Simplify Division Prop

Your Practice Reason Given Addition Prop Simplify Division Prop Solve and Justify Statement -2p – 9 = 10p – 17 +2p +2p -9 = 12p – 17 +17 +17 8 = 12p 8 12 = 12𝑝 12 2 3 = p Reason Given Addition Prop Simplify Division Prop

Ex. 2 Using Distributive Prop Solve and Justify -5(7w+8) = 30 -35w – 40 = 30 +40 +40 -35w = 70 −35𝑤 −35 = 70 −35 w = -2 Given Distributive Prop Addition Prop Simplify Division Prop

Ex. 3 Literal Equations Solve and Justify Solve p(r+1)=n for r pr+p = n -p -p pr = n – p 𝑝𝑟 𝑝 = 𝑛−𝑝 𝑝 r = 𝑛−𝑝 𝑝 Given Distributive prop Subtraction prop Simplify Division prop

Your Practice Given Distributive prop Addition prop Simplify Solve and justify Solve s = 180(n – 2) for n s = 180n – 360 +360 +360 S + 360 = 180n 𝑠+360 180 = 180𝑛 180 𝑠+360 180 =𝑛 Given Distributive prop Addition prop Simplify Division prop

Ex. 4 Identifying Properties 𝑚∠1=𝑚∠3 If BC = XY and XY = 8, then BC = 8 Reflexive Prop of Equality Transitive Prop of Equality