CK12 - Geometry

Two polygonsaresimilarif and only if:

• they havethe samenumberof sides


• for eachanglein eitherpolygonthereis a correspondinganglein the otherpolygonthat is congruent


• the lengthsof all correspondingsidesin the polygonsare proportional

Reminder:Just as we did with congruentfigures,we namesimilarpolygonsaccordingto corresponding
parts.The symbol is usedto represent“is similarto.” Somepeoplecall this “the congruentsign without
the equalspart.”

Example 1

Suppose Basedon this statement,whichanglesare congruentand whichsidesare
proportional?Writetrue congruencestatementsand proportions.

, , and

Rememberthat thereare manyequivalentwaysto writea proportion.The answeraboveis not the only set
of true proportionsyou can createbasedon the givensimilaritystatement.Can you thinkof others?

Example 2

Given:

Whatare the valuesof , ,and in the diagrambelow?

Set up a proportionto solvefor :

Now set up a proportionto solvefor :