Question

prove that the ratio of the areas of two similar triangles is equal to the square of ratio of their medians​

Answer 1

given

tri. ABC is similar to tri. PQR

And AD and PS are median

to prove

ar(Abc) AD^2

------------- = ---------

ar ( PQR) PS^2

proof ..

in tri. abc and tri. pqr

by bpt ....

AB / PQ = BC / QR

AB/PQ = BC/2/QR/2 ......(1)

therefore

AB/PQ = BD/QS .....{by (1)}

so by converse of bpt tri. ABD is similar to tri. PQS

so by bpt ..

AB /PQ = AD/PS ......(2)

by area thrm ...

ar(abc) AB^2

------------- = ----------

ar (pqr) PQ ^2

from equation (2)

ar(abc) AD ^2

------------ = -----------

ar(pqr) PS^2

hence proved

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