is.
LessonSummary
Similarhas a very specificmeaningin geometry. Polygonsare similarif and only if the lengthsof their sides
are proportionaland correspondinganglesare congruent.This issameshapetranslatedinto geometric
terms.
The ratio of the lengthsof correspondingsidesin similarpolygonsis calledthe scalefactor. Lengthsof other
correspondinglinearmeasures,suchas perimeter, diagonals,etc. havethe samescalefactor.
Pointsto Consider
Scalefactorsshowthe relationshipbetweencorrespondinglinearmeasuresin similarpolygons.The story
is not quitethat simplefor the relationshipbetweenthe areasor volumesof similarpolygonsand polyhedra
(three-dimensionalfigures).We’ll studytheserelationshipsin futurelessons.
Similartrianglesare the basisfor the studyoftrigonometry. The fact that the ratiosof the lengthsof corre-
spondingsidesin right trianglesdependsonly on the measureof an angle,not on the size of the triangle,
makestrigonometricfunctionsthe propertyof an angle,as you will studyin Chapter8.
LessonExercises
True or false?
- All equilateraltrianglesare similar.
- All isoscelestrianglesare similar.
- All rectanglesare similar.
- All rhombusesare similar.
- All squaresare similar.
- All congruentpolygonsare similar.
- All similarpolygonsare congruent.
Use the followingdiagramfor exercises8-11.
Giventhat rectangle rectangle.