- AAS trianglecongruencepostulate
- Definitionof congruenttriangles(corre-
spondingpartsare congruent)
7.
Isoscelesand EquilateralTriangles
LearningObjectives
- Proveand use the BaseAnglesTheorem.
- Provethat an equilateraltrianglemustalso be equiangular.
- Use the converseof the BaseAnglesTheorem.
- Provethat an equiangulartrianglemustalso be equilateral.
Introduction
As you can imagine,thereis moreto trianglesthan provingthemcongruent.Thereare manydifferentways
to analyzethe anglesand sideswithina triangleto understandit better. This chapteraddressessomeof
the waysyou can find informationabouttwo specialtriangles.
BaseAnglesTheorem
Anisoscelestriangleis definedas a trianglethat has at leasttwo congruentsides.In this lessonyou will
provethat an isoscelestrianglealso has two congruentanglesoppositethe two congruentsides.The con-
gruentsidesof the isoscelestriangleare calledthelegsof the triangle.The otherside is calledthebase
and the anglesbetweenthe baseand the congruentsidesare calledbaseangles.The anglemadeby the
two legs of the isoscelestriangleis calledthevertexangle.
TheBaseAnglesTheoremstatesthat if two sidesof a triangleare congruent,then their oppositeangles
are also congruent.In otherwords,the baseanglesof an isoscelestriangleare congruent.Note,this theorem
doesnot tell us aboutthe vertexangle.
Example 1
Whichtwo anglesmustbe congruentin the diagrambelow?