**Q) **Sides AB, BC and the median AD of ∆ ABC are respectively proportional to sides PQ, QR and the median PM of another

∆ PQR. Prove that ∆ ABC ~ ∆ 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)

Now by SAS similarity rule,

**Δ ABC ~ Δ PQR……….. Hence proved !**

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