CK12 - Geometry

The lengthof everyside of the first polygonis timesthe lengthof the correspondingside of the other
polygon.

Example 5

Lookat the diagrambelow, where and are similarrectangles.

A.Whatis the scalefactor?

Since , then and are correspondingsides.Since is a rectangle,

you knowthat.

The scalefactoris the ratio of the lengthsof any two correspondingsides.

So the scalefactor(relating to ) is. We now knowthat the lengthof

eachside of is timesthe lengthof the correspondingside in.

Comment:We can turn this relationshiparound“backwards”and talk aboutthe scalefactorrelating

to. This scalefactoris just whichis thereciprocalof the scalefactorrelating

to

B.Whatis the ratio of the perimetersof the rectangles?

is a by rectangle.Its perimeteris.

is a by rectangle.Its perimeteris.

The ratio of the perimetersof to is.

Comment:You see from this examplethat the ratio of the perimetersof the rectanglesis the sameas the
scalefactor. This relationshipfor the perimetersholdstrue in generalfor any similarpolygons.

Ratioof Perimetersof SimilarPolygons

Let’s provethe theoremthat was suggestedby example5.