4. CongruentTriangles....................................................................................................................
TriangleSums
LearningObjectives
- Identifyinteriorand exterioranglesin a triangle.
- Understandand applythe TriangleSum Theorem.
- Utilizethe complementaryrelationshipof acuteanglesin a right triangle.
- Identifythe relationshipof the exterioranglesin a triangle.
Introduction
In the first chapterof this course,you developedan understandingof basicgeometricprinciples.The rest
of this courseexploresspecificideas,techniques,and rulesthat will help you be a successfulproblemsolver.
If you ever wantto reviewthe basicproblemsolvingin geometryreturnto Chapter1. This chapterexplores
trianglesin moredepth.In this lesson,you’llexploresomeof their basiccomponents.
Interiorand ExteriorAngles
Any closedstructurehas an insideand an outside.In geometrywe use the wordsinteriorandexteriorfor
the insideand outsideof a figure.Aninteriordesigneris someonewho furnishesor arrangesobjectsinside
a houseor office. Anexternalskeleton(or exo-skeleton)is on the outsideof the body. So the prefix“ex”
meansoutsideand exteriorrefersto the outsideof a figure.
The termsinteriorand exteriorhelp whenyou needto identifythe differentanglesin triangles.The three
anglesinsidethe trianglesare calledinteriorangles.On the outside,exterioranglesare the anglesformed
by extendingthe sidesof the triangle.The exteriorangleis the angleformedby one side of the triangleand
the extensionof the other.