CK12 - Geometry

Ratioof the Perimetersof SimilarPolygons: If and are two similarpolygons,

eachwith sidesand the scalefactorof the polygonsis , thenthe ratioof the

perimetersof the polygonsis.

•

Given: and are two similarpolygons,eachwith sides

The scalefactorof the polygonsis

• Prove:The ratio of the perimetersof the polygonsis

Statement Reason

1. Given


2. and are similarpolygons,eachwith sides


3. The scalefactorof the polygonsis 2. Given


4. Given(polygonshave sides
   each)

3.Let and bethelengths

of correspondingsidesof and

4. 
   
   
   
   4. Definitionof scalefactor
   
   
   5. Definitionof perimeter
   
   
   
   


5. Perimeterof


6. 
   
   
   
   6. Substitution
   
   
   7. DistributiveProperty
   
   
   
   


7. 
   


8. , the perimeterof 8. Definitionof perimeter

Comment:The ratio of the perimetersof any two similarpolygonsis the sameas the scalefactor. In fact,
the ratio ofany two correspondinglinearmeasuresin similarfiguresis the sameas the scalefactor. This
appliesto correspondingsides,perimeters,diagonals,medians,midsegments,altitudes,etc.

As we’ll see in an upcominglesson,this is definitelynot truefor theareasof similarpolygons.The ratio of
the areasof similarpolygons(that are not congruent)isnotthe sameas the scalefactor.

Example 6

. The perimeterof is 150.

Whatis the perimeterof?

The scalefactorrelating to is. Accordingto the Ratioof the Perimeter's

Theorem,the perimeterof is of the perimeterof. Thus,the perimeterof