CK12 - Geometry

• AdditionPropertyof Equality: If , then.

Translation:You can add the samenumberto both sidesof an equation.

Example:If , then.

• MultiplicationPropertyof Equality: If , then

Translation:You can multiplythe samenumberon both sidesof an equation.

Example:If , then.

Keepin mindthat theseare propertiesaboutnumbers. As you go furtherinto geometry, you can applythe
propertiesof equalityto anythingthat is a number:lengthsof segmentsand anglemeasures,for example.

Propertiesof Congruence

Let’s reviewthe definitionsof congruentsegmentsand angles.

if and only if.

CongruentSegments:

Rememberthat, although and aresegments, and arelengths

of thosesegments,meaningthat and arenumbers. The propertiesof

equalityapplyto and.

CongruentAngles: if and only if =

The commentaboveaboutsegmentlengthsalso appliesto anglemeasures.The

propertiesof equalityapplyto and.

Any statementaboutcongruentsegmentsor congruentanglescan be translateddirectlyinto a statement
aboutnumbers.This meansthat eachpropertyof equalityhas a correspondingpropertyof congruentseg-
mentsand a correspondingpropertyof congruentangles.

Hereare someof the basicpropertiesof equalityand the correspondingcongruenceproperties.

Giventhat and are real numbers.

ReflexivePropertyof Equality:

ReflexivePropertyof Congruenceof Segments:

ReflexivePropertyof Congruenceof Angles:

SymmetricPropertyof Equality: If , then.

If , then

SymmetricPropertyof Congruenceof Segments: