Chapter 2Section 2.5

Reasoning With Properties of Algebra

Algebraic Properties of Equality

• Let a, b,c be real numbers– Addition property of equality

• If a = b, then a + c = b + c

– Subtraction property of equality• If a = b, then a - c = b – c

– Multiplication property of equality• If a = b, then ac = bc

– Division property of equality• If a = b and c 0, then a c = b c

Algebraic Properties of Equality

• Let a, b,c be real numbers– Reflexive property of equality

• For any real number a, a = a

– Symmetric property of equality• If a = b, then b = a

– Transitive property of equality• If a = b and b = c, then a = c

– Substitution property of equality• If a = b, then a can be substituted for b in any

equation or expression

Use the property to complete the statement

1. Reflexive property of equality: mT = m T

2. Transitive property: If KL = MN and _____ = RW, then _____ MN KL = RW

3. Addition property of equality: If x = 5, then 17 + x = ______17 + 5

4. Symmetric property of equality: If BC = RL, then ______RL = BC

5. Substitution property of equality:

If mA = 45 and mB = mA + 90 then____mB = 45 + 90 = 135

6. Multiplication property of equality: If mA = 45, then _____

(mA) = 151

3

Complete the argument, giving a reason for each step

Addition Property of =Distributive Property

Subtraction Property of =

Complete the argument, giving a reason for each step

Addition Property of =Addition Property of =

Division Property of =

Complete the argument, giving a reason for each step

Substitution prop of =Segment Addition Postulate

Substitution property of =

Complete the argument, giving a reason for each step

a. Reflexive prop of =

Given

b. Addition property of =c. Angle Addition postulated. Angle Addition postulate

e. Substitution property of =

Complete the argument, giving a reason for each step

a. Definition linesGiven

b. Definition linesc. Substitution property of =

HW #20Pg. 108-109 #1-29