**Q) **In the given figure, CD and RS are respectively the medians of Δ ABC and Δ PQR. If Δ ABC ~ Δ PQR then prove that:

(i) Δ ADC ~ Δ PSR

(ii) AD x PR = AC x PS

**Ans:**

(i) Its given that:

- CD is median of ΔABC
- RS is median of ΔPQR
- ΔABC∼ΔPQR

AB = 2AD as CD is the median

and PQ=2PS as RS is the median

Since ΔABC∼ΔPQR

=

=

=

ΔADC∼ΔPSR ….. **Hence proved**

(ii) Since we just proved that, ΔADC∼ΔPSR

=

AD x PR = AC x PS ….. **Hence proved**