**Q) **Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of **Δ** PQR. Show that **Δ** ABC ~ **Δ** PQR.

**Ans: **

Given that, In Δ ABC and Δ PQR,

Since AD is median of BC, hence BC = 2BD

Similarly, PM is median of QR, hence QR = 2QM

or

** Δ** ABD ~ **Δ** PQM

Hence, ∠ B = ∠ Q ……………. (i)

Now In Δ ABC and Δ PQR, we know that,

or (given)

∠ B = ∠ Q from equation (i)

**Δ ABC ~ Δ PQR……….. Hence proved**