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Question
In the given figure, ΔPQR is a right-angled triangle with ∠PQR = 90°. QS is perpendicular to PR. Prove that pq = rx.
Solution
Given: ∠PQR = 90° and QS ⊥ PR.
So, ∠QSR = ∠QSP = 90°
Now, in ΔPQR and ΔQSR,
∠QRP ≅ ∠SRQ ......[Common angle]
∠PQR ≅ ∠QSR ......[Each angle is equal to 90°]
So, according to the AA similarity criterion,
ΔPQR ∼ ΔQSR
∴ `(PR)/(QR) = (PQ)/(QS)` .....[C.S.S.T.]
⇒ `r/q = p/x`
⇒ x × r = p × q
⇒ pq = rx
Hence proved.
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