Question

Sides AB and. AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ΔABC ~ ΔPQR.

Answer 1

Construction: Produce AD to E such that AD = DE and produce PM to N such that PM = MN. Join BE, CE, QN, RN.
proof: Quadrilateral  ABEC and PQNR are ||^gm  because their diagonals bisect each other at D and M respectively