To begina Venn Diagram,you mustfirst drawa largeellipserepresentingthe biggestcategory. In this
case,that will be quadrilaterals.
Now, one classof quadrilateralsare parallelograms—allquadrilateralswith oppositesidesparallel.But, not
all quadrilateralsare parallelograms:kites haveno pairsof parallelsides,and trapezoidsonly haveone pair
of parallelsides.In the diagramwe can showthis as follows:
Okay, we are almostthere,but thereare severaltypesof parallelograms.Squares,rectangles,and rhombi
are all typesof parallelograms.Also,underthe categoryof trapezoidswe needto add isoscelestrapezoids.
The completedVenn diagramis like this:
You can use this Venn Diagramto quicklyanswerquestions.For instance,is everysquarea rectangle?
(Yes.) Is everyrhombusa square?(No, but someare.)
Strategiesfor Shapeson a CoordinateGrid
You havealreadypracticedsomeof the tricksfor analyzingshapeson a coordinategrid. You actuallyhave
all of the tools you needto classifyany quadrilateralplacedon a grid. To find out whethersidesare congruent,
you can use the distanceformula.
Distance Formula: Distance between points