Whatdoesthis say abouta segmentand its imagein a dilation?It says that the imageof a segmentis another
segment timesthe lengthof the originalsegment.If a polygonhad severalsides,eachside of the image
polygonwouldbe timesthe lengthof its correspondingside in the originalpolygon.
Conclusion: If a polygonis dilated,the correspondingsidesof the imagepolygonand the originalpolygon
are proportional.So half the battleis over.
Part 2: CongruentAngles
Let’s look at the slopesof the sidesof two angles, and.
slopeof
slopeof
slopeof
slopeof
Since and havethe sameslope,they are parallel.The sameis true for and. We
knowthat if the sidesof two anglesare parallel,then the anglesare congruent.This givesus:
Conclusion: If a polygonis dilated,the correspondinganglesof the imagepolygonand the originalpolygon
are congruent.So the battleis now over.
FinalConclusion: If a polygonis dilated,the originalpolygonand the imagepolygonare similar, because
they haveproportionalside lengthsand congruentangles.A dilationis a similaritytransformation.
LessonSummary
Dilationsroundout our studyof geometrictransformations.Unliketranslations,rotations,and reflections,
dilationsare not congruencetransformations.Theyare similaritytransformations.If a dilationis appliedto
a polygon,the imageis a similarpolygon.
Pointsto Consider
We limitedour studyof dilationsto thosethat havepositivescalefactors.To explorefurther, you mightex-
perimentwithnegativescalefactors.
Tech Note- GeometrySoftwareUse your geometrysoftwareto exploredilationswith negativescalefactors.Exploration 1- Plot two points.
- Selectone of the pointsas the centerof dilation.