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:

1. CD is median of ΔABC
2. RS is median of ΔPQR
3. 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