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AAA Similarity

In the given ...

Question

In the given figure, AB // EF // DC; AB = 67.5 cm, DC = 40.5 cm and AE = 52.5 cm.
(i) Name the three pairs of similar triangles.
(ii) Find the lengths of EC and EF.

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Solution

(i) The three pair of similar triangles are:

BEF and BDC

CEF and CAB

ABE and CDE

(ii) Since, ABE and CDE are similar,

$fraction numerator A B over denominator C D end fraction equals fraction numerator A E over denominator C E end fraction fraction numerator 67.5 over denominator 40.5 end fraction equals fraction numerator 52.5 over denominator C E end fraction C E equals 31.5 space c m$

Since, CEF and CAB are similar,

$fraction numerator C E over denominator C A end fraction equals fraction numerator E F over denominator A B end fraction fraction numerator 31.5 over denominator 52.5 plus 31.5 end fraction equals fraction numerator E F over denominator 67.5 end fraction fraction numerator 31.5 over denominator 84 end fraction equals fraction numerator E F over denominator 67.5 end fraction E F equals fraction numerator 2126.25 over denominator 84 end fraction E F equals 405 over 16 space c m$

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In the given figure $A B ∥ E F ∥ D C$ ; AB = 67.5 cm. DC = 40.5 cm and AE = 52.5 cm. Find the length of EF.

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