CK12 - Geometry

Now quadrilateral is a parallelogramby construction.Thus,the theoremaboutoppositesidesof

a parallelogramtells us The trianglemidsegmenttheoremtells us that

or

So,

by the segmentadditionpostulate

by substitution

by factoringout and cancelingthe 2

by the segmentadditionpostulate.Whichis exactlywhatwe wantedto show!

Kites

LearningObjectives

• Identifythe relationshipbetweendiagonalsin kites.


• Identifythe relationshipbetweenoppositeanglesin kites.

Introduction

Amongall of the quadrilateralsyou havestudiedthus far, kitesare probablythe mostunusual.Kiteshave
no parallelsides,but they do havecongruentsides.Kitesare definedby two pairsof congruentsidesthat
are adjacentto eachother, insteadof oppositeeachother.

Avertexangleis betweentwo congruentsidesand anon-vertexangleis betweensidesof differentlengths.

Kiteshavea few specialpropertiesthat can be provenand analyzedjust as the otherquadrilateralsyou
havestudied.This lessonexploresthoseproperties.

Diagonalsin Kites

The relationshipof diagonalsin kites is importantto understand.The diagonalsare not congruent,but they
are alwaysperpendicular. In otherwords,the diagonalsof a kite will alwaysintersectat right angles.

Theorem:The diagonalsof a kite are perpendicular