CK12 - Geometry

take on new life whenexpressedin the contextof geometry.

Propertiesof Equality

All thingsbeingequal,in mathematicsthe word“equal”means“the sameas.” To be precise,the equalsign
meansthat the expressionon the left of the equalsign and the expressionon the right representthe
samenumber. So equalityis specificallyaboutnumbers—numbersthat may be expresseddifferentlybut
are in fact the same.

Someexamples:

•

•

Basicpropertiesof equalityare quitesimpleand you are probablyfamiliarwith themalready. Theyare listed
here in formallanguageand then translatedto commonsenseterms.

Propertiesof Equality

For all real numbers , , and :

• ReflexiveProperty:

That is, any numberisequaltoitself,orthe sameasitself.

Example:

• SymmetricProperty: If then.

You can read an equalityleft to right,or right to left.

Example:If then

Example:If , then.

Sometimesit is moreconvenientto write than. The symmetricpropertyallowsthis.

• TransitiveProperty: If and then.

Translation:If thereis a “chain”of linkedequations,then the first numberis equalto the last number. (You
can provethat this appliesto morethan two equalitiesin the reviewquestions.)

Example:If and , then.

As a reminder, hereare somepropertiesof equalitythat you usedheavilywhenyou learnedto solve
equationsin algebra.

• SubstitutionProperty: If then can be put in placeof anywhereor everywhere.

Example:Giventhat and that. Then.