Chapter 2 Chapter 2 Lesson 4Lesson 4Objective: To

connect reasoning in algebra to geometry.

Properties of Properties of EqualityEquality

•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 and c≠0, then a/c = b/c

•Reflexive Property 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 b can replace a in any expression

••

B

O C

Angle Addition Angle Addition PostulatePostulate

The Distributive The Distributive PropertyProperty

a(b+c) = ab + ac

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

A •

Solve for x and justify each step.

Given: Given: m AOC = 139

Example 1:Example 1:

• ••

AB

CO

x°(2x + 10)°

m AOB + m BOC = m AOC Angle Addition Postulate

x + 2x + 10 = 139 Substitution Property 3x + 10 = 139 Simplify 3x = 129 Subtraction Property

of = x = 43 Division Property of =

Example 2:Example 2:Justify each step used to solve 5x – 12 = 32 + x5x – 12 = 32 + x for x.

5x = 44 + x

4x = 44

X = 11

Addition Property of Equality

Subtraction Property of Equality

Division Property of Equality

• ••

KM

NL

(2x + 40)°4x°

Example 3:Example 3:Fill in each missing reason.

LM bisects KLN Given

m MLN = m KLM Definition of angle bisector

4x = 2x + 40 _____________________

2x = 40 _____________________

x = 20 _____________________

Substitution Prop.

Subtraction Prop. of Equality

Division Prop. Of Equality

Example 4:Example 4:Solve for yy and justify each step.

2y 3y-9

A B CGiven: AC = 21

AB + BC = AC

2y + (3y – 9) = 21

5y – 9 = 21

5y = 30

Y = 6

Segment Addition Postulate

Substitution Property

Simplify

Addition Property of Equality

Division Property of Equality

Properties of Properties of CongruenceCongruence

Reflexive Property AB AB

A A

Symmetric Property If AB CD, then CD AB

If A B, then B A

Transitive Property If AB CD and CD EF, then AB EF

If A B and B C, then A C.

Example 5:Example 5:Name the property of equality or congruence that justifies each statement.

a. K K Reflexive Property of Congruence

b. If 2x – 8 = 10, then 2x = 18

Addition Property of Equality

c. If x = y and y + 4 = 3x, then x + 4 = 3x.

Substitution Property of Equality

d. If RS TW and TW PQ, then RS PQ. Transitive Property of Congruence

HomeworkHomework

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