Lesson 2-4Reasoning in Algebra

Check Skills You’ll Need

1. Name 1 in two other ways.2. Name the vertex of 2.3. If 1 2 , name the bisector of

AOC. 4. If m AOC = 90 and m 1 =45,

find m 25. If m AOC = 90, name two

perpendicular rays.

A

O1

2 B

C

Properties of Equality

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 a c = b c.Division Property If a = b, then a/c = b/c.Reflexive Property a = aSymmetric Property If a = b, then b = aSubstitution Property If a = b, then you may replace b with

a inany expression.Transitive Property If a = b and b = c, then a = c.Distributive Property a(b + c) = ab + ac

Segment Addition Postulate

If three points A, B, and C are collinear and B is between A and C, then A + B = AC

Angle Addition Postulate

If point B is in the interior of AOC, then m AOB + m BOC = m AOC.

A B C

AO

B

C

Example: Justifying Steps in Solving an Equation

Solve for x and justify each stepGiven: m AOC = 139

m AOB + m BOC = m AOC x + 2x + 10 = 139 3x +10 = 139 3x = 129 x = 43

x0

(2x + 10) 0A

O

B

C

Angle Addition PostulateSubstitution PropertySimplifySubtraction PropertyDivision Property

Example: Justifying Steps in Solving an Equation

Fill in the missing reason.Given: LM bisects KLN

LM bisects KLNm MLN = m KLM 4x = 2x + 40 2x = 40 x = 20

(2x + 40)04x 0

KL

M

NGivenDefinition of a bisectorSubstitutionSubtraction PropertyDivision Property

Justifying Steps in Solving an Equation

Solve for y and justify each step.Given: AC = 21

AB + BC = AC2y + (3y – 9) = 215y – 9 = 215y = 30y = 6

A B C

2y 3y - 9

segment addition postulatesubstitution simplifyaddition propertydivision property

Properties of Congruence

Reflexive Property AB BA A ASymmetric PropertyIf AB CD, then CD AB.If A B, then B A.Transitive PropertyIf AB CD, and CD EF, then AB EF.If A B and B C, then A C.

Using Properties of Equality and Congruence

K KIf 2x – 8 = 10, then 2x = 18If RS TW and TW PQ, then RS PQIf m A = m B, then m B = m AXY YXIf m A = 45 and 45 = m B, then m A = m B

ReflexiveAddition PropertyTransitiveSymmetricSymmetric

Substitution

It’s TEST TIME

folks