2.4 Algebraic Reasoning

What We Will LearnO Use algebraic properties of equality

to justify steps in solvingO Use distributive property to justify

steps in solvingO Use properties of equality involving

segment lengths and angle measures

Needed VocabO Addition Prop: If a = b, then a+c = b+cO Subtraction Prop: a-c = b-cO Multiplication prop: ac = bcO Division prop: O Substitution prop: If a = b, then a can be

substituted for b (or b for a) in any equation or expression

O Distributive prop: a(b+c) = ab + acO Reflexive Prop of Equality: a = aO Symmetric Prop of Equality: If a = b, then b = aO Transitive Prop of Equality: If AB = CD and CD =

EF, then AB = EF.

Ex. 1 Justifying StepsO Start of proofsO Solve and justifyO Statement O 6x – 11 = -35O +11 +11O 6x = -24O O x = -4

O ReasonO GivenO Addition PropO SimplifyO Division Prop

Your PracticeO Solve and JustifyO StatementO -2p – 9 = 10p – 17O +2p +2pO -9 = 12p – 17 O +17 +17 O 8 = 12pO O = p

O ReasonO GivenO Addition PropO SimplifyO Addition PropO SimplifyO Division Prop

Ex. 2 Using Distributive Prop

O Solve and JustifyO -5(7w+8) = 30O -35w – 40 = 30O +40 +40O -35w = 70

O w = -2

O GivenO Distributive PropO Addition PropO SimplifyO Division Prop

Ex. 3 Literal EquationsO Solve and JustifyO Solve p(r+1)=n

for rO pr+p = n O -p -pO pr = n – p

O r =

O GivenO Distributive propO Subtraction propO SimplifyO Division prop

Your PracticeO Solve and justifyO Solve s = 180(n –

2) for nO s = 180n – 360 O +360 +360O S + 360 = 180n

O GivenO Distributive propO Addition propO SimplifyO Division prop

Ex. 4 Identifying Properties

O If BC = XY and XY = 8, then BC = 8

O Reflexive Prop of Equality

O Transitive Prop of Equality