CK-12 Geometry Concepts

2.7. Properties of Equality and Congruence http://www.ck12.org

AB+BC=AC Segment Addition Postulate

8 + 17 = 20 Substitution PoE

256 = 20 Combine like terms

Because the two sides are not equal,A,BandCare not collinear.

Example C

Ifm^6 A+m^6 B= 100 ◦andm^6 B= 40 ◦, prove that^6 Ais an acute angle.

We will use a two-column format, with statements in one column and their corresponding reasons in the next. This
is formally called a two-column proof.

TABLE2.18:

Statement Reason

1.m^6 A+m^6 B= 100 ◦andm^6 B= 40 ◦ Given(always the reason for using facts that are told to

us in the problem)

2.m^6 A+ 40 ◦= 100 ◦ Substitution PoE

3.m^6 A= 60 ◦ Subtraction PoE

4.^6 Ais an acute angle Definition of an acute angle,m^6 A< 90 ◦

Watch this video for help with the Examples above.

MEDIA

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CK-12 Foundation: Chapter2PropertiesofEqualityandCongruenceB

Vocabulary

Theproperties of equalityandproperties of congruenceare the logical rules that allow equations to be manipu-
lated and solved.

Guided Practice

Use the given property or properties of equality to fill in the blank.x,y, andzare real numbers.

1. Symmetric: Ifx=3, then __.


2. Distributive: If 4( 3 x− 8 ), then __.


3. Transitive: Ify=12 andx=y, then __.

Answers:

1. 3=x


2. 12x− 32