CK12 - Geometry

UsingCongruentTriangles

LearningObjectives

• Applyvarioustrianglescongruencepostulatesand theorems.


• Knowthe waysin whichyou can provepartsof a trianglecongruent.


• Find distancesusingcongruenttriangles.


• Use constructiontechniquesto createcongruenttriangles.

Introduction

As you can see, thereare manydifferentwaysto provethat two trianglesare congruent.It is importantto
knowall of the differentway that can provecongruence,and it is importantto knowwhichcombinationsof
sidesand anglesdonotprovecongruence.Whenyou provepropertiesof polygonsin later chaptersyou
will frequentlyuse

CongruenceTheoremReview

As you havestudiedin the previouslessons,thereare five theoremsand postulatesthat providedifferent
waysin whichyou can provetwo trianglescongruentwithoutcheckingall of the anglesand all of the sides.
It is importantto knowthesefive ruleswell so that you can use themin practicalapplications.

Name Correspondingcongruentparts Doesit provecongruence?

SSS Threesides Yes

SAS Two sidesand the anglebetweenthem Yes

ASA Two anglesand the side betweenthem Yes

AAS Two anglesand a side not betweenthem Yes

HL A hypotenuseand a leg in a right triangle Yes

No—itwill createa similartriangle,but not of the same

size

AAA Threeangles

SSA Two sidesand an anglenot betweenthemNo—thiscan createmorethan one distincttriangle

Whenin doubt,thinkaboutthe modelswe created.If you can constructonly one possibletrianglegiventhe
constraints,then you can provecongruence.If you can createmorethan one trianglewithinthe giveninfor-
mation,you cannotprovecongruence.

Example 1

Whatrule can provethat the trianglesbeloware congruent?

A. SSS

B. SSA