CK-12 Geometry-Concepts

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

2.7 Properties of Equality and Congruence

Here you’ll review the properties of equality you learned in previous concepts, be introduced to the properties of
congruence, and learn how to use these properties.

What if you wanted to solve an equation and justify each step? What mathematical properties could you use in your
justification? After completing this Concept, you be able to see how the properties of equality from Algebra I relate
to geometric properties of congruence.

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CK-12 Foundation: Chapter2PropertiesofEqualityandCongruenceA

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James Sousa: Introduction to Proof Using Properties of Equality

Guidance

The basic properties of equality were introduced to you in Algebra I. Here they are again:

Forallrealnumbersa,b,andc:

TABLE2.16:

Examples

Reflexive Property of Equality a=a 25 = 25

Symmetric Property of Equality a=bandb=a m^6 P= 90 ◦or 90◦=m^6 P

Transitive Property of Equality a=bandb=c, thena=c a+ 4 =10 and 10= 6 +4, thena+

4 = 6 + 4

Substitution Property of Equality Ifa=b, thenbcan be used in place

ofaand vise versa.

Ifa=9 anda−c=5, then 9−c= 5

Addition Property of Equality Ifa=b, thena+c=b+c. If 2x=6, then 2x+ 5 = 6 + 11