Question

In the given figure, ΔPQR is a right-angled triangle with ∠PQR = 90°. QS is perpendicular to PR. Prove that pq = rx.

Answer 1

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.