6. Quadrilaterals...............................................................................................................................
InteriorAngles
LearningObjectives
- Identifythe interioranglesof convexpolygons.
- Find the sumsof interioranglesin convexpolygons.
- Identifythe specialpropertiesof interioranglesin convexquadrilaterals.
Introduction
By this point,you havestudiedthe basicsof geometryand you’vespentsometime workingwith triangles.
Now you will beginto see somewaysto applyyour geometricknowledgeto otherpolygons.This chapter
focuseson quadrilaterals—polygonswith four sides.
Note:Throughoutthis chapter, any time we talk aboutpolygons,we will assumethat we are talkingabout
convexpolygons.
InteriorAnglesin ConvexPolygons
The interioranglesare the angleson the insideof a polygon.
As you can see in the image,a polygonhas the samenumberof interioranglesas it doessides.
SummingInteriorAnglesin ConvexPolygons
You havealreadylearnedthe TriangleSum Theorem.It statesthat the sum of the measuresof the interior
anglesin a trianglewill alwaysbe. Whataboutotherpolygons?Do they havea similarrule?
We can use the trianglesum theoremto find the sum of the measuresof the anglesfor any polygon.The
first step is to cut the polygoninto trianglesby drawingdiagonalsfrom one vertex.Whendoingthis you must
makesure noneof the trianglesoverlap.