Question

prove that the ratio of the area of two similar triangles is equal to the square of the ratio of their corresponding medians

Answer 1

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Answer 2

Since ratio of similiar triangle is equal to ratio of square of corresponding sides.
Therefore ar(triABC) upon (tri DEF) is equal to
AB sq upon DE sq .....(1)
Now, tri ABC is similiar to triDEF
ABupon DE is equal to BC up
on EF
ABupon DE is equal to 2BP upon 2EQ is equal to BP upon EQ.....(2)
ABupon DE is equal toBP upon EQ and angle B
is eqial to angle E
By SAS we have
BP upon EQ is equal to AP upon DQ ....(3)
From (2) and (3)
ABupon DE is equal to AP upon DQ
AB sq upon DEsq is equal to APsq upon DQsq.(4)
From (1) and(4)
ar(tri ABC) upon ar(tri DEF) is equal to APsq upon DQsq.