Question

1. From the adjoining figure, prove that ∆PQR ~ ∆ ABC. Hence prove that
PR/ AC = √
PQ /AB × QR /BC.​

Answer 1

Given :- ∆PQR ~ ∆ ABC.

To Prove :-

• PR/ AC = √{(PQ/AB) × (QR /BC)} .

Solution :-

since ∆PQR ~ ∆ ABC , so, their corresponding sides are in same proportion .

then,

→ PR/AC = PQ/AB = QR/BC = Let k .

putting values in given equation we get,

→ PR/ AC = √{(PQ/AB) × (QR /BC)}

→ k = √(k * k)

→ k = √(k²)

→ k = k .

therefore,

→ PR/ AC = √{(PQ/AB) × (QR /BC)} (Proved).

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