CK12 - Geometry

to congruencethat will help you solvegeometryproblemsas well.

Thereflexivepropertyof congruencestatesthat any shapeis congruentto itself.This may seemobvious,
but in a geometricproof,you needto identifyeverypossibilityto help you solvea problem.If two triangles
sharea line segment,you can provecongruenceby the reflexiveproperty.

In the diagramabove,you can say that the sharedside of the trianglesis congruentbecauseof the reflexive

property. Or in otherwords,.

Thesymmetricpropertyof congruencestatesthat congruenceworksfrontwardsand backwards,or in

symbols,if then.

Thetransitivepropertyof congruencestatesthat if two shapesare congruentto a third,they are also

congruentto eachother. In other words,if , and , then

. This propertyis very importantin identifyingcongruencebetweendifferentshapes.

Example 4

Whichpropertycan be usedto provethe statementbelow?

If and , then.

A. reflexivepropertyof congruence

B. identitypropertyof congruence

C. transitivepropertyof congruence

D. symmetricpropertyof congruence

The transitivepropertyis the one that allowsyou to transfercongruenceto differentshapes.As this states
that two trianglesare congruentto a third,they mustbe congruentto eachotherby the transitiveproperty.
The correctansweris C.

LessonSummary

In this lesson,we exploredcongruentfigures.Specifically, we havelearned:

• How to definecongruencein triangles.


• How to createaccuratecongruencestatements.


• To understandthat if two anglesof a triangleare congruentto two anglesof anothertriangle,the remaining
  angleswill also be congruent.