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) Δ ADC ~ Δ PSR

Step 1: Since it is 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

Step 2: Since Δ ABC ∼ Δ PQR

∴ =

∴ =

∴ =

∴ Δ ADC ∼ Δ PSR ….. Hence proved !

(ii) AD x PR = AC x PS:

Step 3: Since we just proved that, Δ ADC ∼ Δ PSR

∴ =

∴  AD x PR = AC x PS ….. Hence proved

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