CK12 - Geometry

congruencestatementsinto numberstatements,and use the propertiesof equality.

EqualityProperties

Reminder:Hereare someof the basicpropertiesof equality. Theseare postulates—noproofneeded.For
eachof thesethereis a correspondingpropertyof congruencefor segments,and one for angles.Theseare
theorems—we’llprovethem.

Propertiesof Equalityfor real numbers , and.

• Reflexive


• Symmetric If then


• Transitive If and , then

Thesepropertiesare convertibles;we can convertthemquicklyand easilyinto congruencetheorems.

Note that diagramsare neededto provethe congruencetheorems.Theyare aboutanglesand segments...ALL
anglesand segments,whereverand wheneverthey are found.No specialsetting(diagram)is needed.

SegmentCongruenceProperties

In this sectionwe’ll provea seriesof segmenttheorems.

Reflexive:

Statement Reason

1. ReflexivePropertyof Equality

2. Definitionof congruentsegments

Symmetric: If , then

Given:

Prove:

Statement Reason

1. Given


2. Definitionof congruentsegments


3. SymmetricPropertyof Equality


4. Definitionof congruentsegments

Transitive: If and , then