Question

prove that corresponding medians of two similar triangles are proportional to corresponding sides of the triangle

Answer 1

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Answer 2

→In ΔABC and ΔPQR, BM and QN are two medians of these two triangles.

So, AM=MC

PN=NR

→In ΔABM and ΔPQN

∠A=∠P

$\frac{AB}{PQ}=\frac{AM}{PN}$→→[ΔABC ~ ΔPQR,]

So, ΔABM ~ ΔPQN→→→[SAS]

∴ $\frac{AB}{PQ}=\frac{BM}{QN}=\frac{BC}{QR}=\frac{AC}{PR}$