If AD and PM are medians of triangles ABC and PQR, respectively whereΔ ABC ~ Δ PQR, prove that

It is given that ΔABC is similar to ΔPQR

We know that the corresponding sides of similar triangles are in proportion

(i)

Also, ∠A = ∠P

∠B = ∠Q

∠C = ∠R (ii)

Since AD and PM are medians, they divide their opposite sides

BD = and,

QM = (iii)

From (i) and (iii), we get

(iv)

In ΔABD and ΔPQM,

∠B = ∠Q [Using (ii)]

[Using (iv)]

ΔABD ΔPQM (By SAS similarity)