Question

If AD and PM are medians of triangles ABC and PQR, respectively where

Answer 1

It is given that ΔABC ∼ ΔPQR

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

∴ … (1)

Also, ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R … (2)

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

∴ … (3)

From equations (1) and (3), we obtain

… (4)

In ΔABD and ΔPQM,

∠B = ∠Q [Using equation (2)]

[Using equation (4)]

∴ ΔABD ∼ ΔPQM (By SAS similarity criterion)

⇒