- Use scalemodelsor scaledrawings.
Introduction
We’ll beginwith a quickreviewof someimportantfeaturesof similarpolygons.You rememberthat we
studiedsimilarfiguresratherextensivelyin Chapter7. Thereyou learnedaboutscalefactorsand perimeters
of similarpolygons.In this sectionwe’ll take similarfiguresone step farther. We’ll see that the areasof
similarfigureshavea very specificrelationshipto the scalefactor—butit’s just a bit tricky!We wrapup the
sectionwith somethoughtson why livingthingsare the “right”size, and whatgeometryhas to do with that!
Review- ScaleFactorsand Perimeter
Example 1
The diagrambelowshowstwo rhombi.a.Are the rhombisimilar?How do you know?Yes.- The sidesare parallel,so the correspondinganglesare congruent.
- Usingthe PythagoreanTheorem,we can see that eachside of the smallerrhombushas a lengthof
, and eachside of the largerrhombushas a lengthof.- So the lengthsof the sidesare proportional.
- Polygonswith congruentcorrespondinganglesand proportionalsidesare similar.