2.4 Reasoning with Properties from Algebra

Algebraic 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 ac = bc.

• Division property: If a=b, and c≠0, then a/c = b/c.

Writing reasons

5 18 3 2

2 18 2

2 20

10

x x

x

x

x

GIVEN

Subtraction Property of Equality

Addition Property of Equality

Division Property of Equality

Solve• Solve 5x – 18 = 3x + 2 and explain each step

in writing. 5x – 18 = 3x + 2 2x – 18 = 2 2x = 20 x = 10

Subtraction p. of e.Addition p. of e.Division p. of e.

More properties of equality

• Reflexive property: For any real number a, 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 a can be

substituted for b in any equation or expression.

Writing Reasons

55 3(9 12) 64z z Given

55 27 36 64 z z

28 36 64 z

28 28z

1z

Distr. Property

Combine Like Terms

Add POE

Div POE

Properties of EqualitySegment Length

Angle Measure

Reflexive AB = AB m<A = m<A

Symmetric If AB = CD, then CD = AB.

If m<A = m<B, then m<B=m<A.

Transitive If AB = CD and CD = EF, then AB=EF.

If m<A = m<B and m<B=m<C, then m<A=m<C.

Given AB=CD, show that AC=BD

A B C D

AB=CD

AB + BC = CD + BC

AB + BC = AC

BC + CD = BDAC = BD

Given

Addition Prop of Equality

Segment Addition Postulate

Segment Addition Postulate

Substitution Prop of Equality

Statements Reasons

1

2 34

Given: 1 2 3 180m m m

1 2 93m m

3 4 180m m

Find: 4m

Review• Let p be “a shape is a triangle” and let q be

“it has an acute angle”.– Write the contrapositive of p q.

– Write the inverse of p q.