Question

In the given triangle P,Q and R are the mid points of sides AB ,BC and AD respectively. Prove that triangle PQR is similar to triangle ABC.

Answer 1

In Tri ABC and Tri PQR

AB=2PQ

PQ/AB= 1:2____1

BC=2QR

QR/BC= 1:2____2

AC=2PR

PR/AC= 1:2____3

Therefore, From 1,2,3

PQ/AB = QR/BC = PR/AC

In Tri PQR and Tri ABC

PQ/AB = QR/BC = PR/AC (proved above)

Tri PQR ~ Tri ABC