- Describethe relationshipbetweenthe two diagonalsin a parallelogram.
Introduction
Now that you havestudiedthe differenttypesof quadrilateralsand their definingcharacteristics,you can
examineeachone of themin greaterdepth.The first shapeyou’lllook at morecloselyis the parallelogram.
It is definedas a quadrilateralwith two pairsof parallelsides,but thereare manymorecharacteristicsthat
makea parallelogramunique.
OppositeSidesin a Parallelogram
By now, you recognizethat thereare manytypesof parallelograms.Theycan look like squares,rectangles,
or diamonds.Eitherway, oppositesidesare alwaysparallel.One of the mostimportantthingsto know,
however, is that oppositesidesin a parallelogramare also congruent.
To test this theory, you can use piecesof stringon your desk.Placetwo piecesof stringthat are the same
lengthdownso that they are parallel.You’ll noticethat the only way to connectthe remainingverticeswill
be two parallel,congruentsegments.Therewill be only one possiblefit giventwo lengths.
Try this againwith two piecesof stringthat are differentlengths.Again,lay themdownso that they are
parallelon your desk.Whatyou shouldnoticeis that if the two segmentsare differentlengths,the missing
segments(if they connectthe vertices)will not be parallel.Therefore,it will not createa parallelogram.In
fact, thereis no way to constructa parallelogramif oppositesidesaren’tcongruent.
So, eventhoughparallelogramsaredefinedby their paralleloppositesides,one of theirpropertiesis that
oppositesidesbe congruent.
Example 1
Parallelogram is shownon the followingcoordinategrid. Use the distanceformulato showthat
oppositesidesin the parallelogramare congruent.