Question

In the fig,PQR and QST are two right triangles ,right angled at R and T respectively .Prove that QR= QS= QP× QT

Answer 1

QR * QS  = QP* QT, PQR and QST are two right triangles ,right angled at R and T respectively

Step-by-step explanation:

Correction

QR * QS  = QP* QT

in ΔPQR  & ΔSQT

∠R = ∠T = 90°

∠Q = ∠Q  (common)

=>  ΔPQR ≈ ΔSQT

=> QP/QS  = QR/QT  = PR/ST

QP/QS  = QR/QT

=> QP * QT = QR * QS

=> QR * QS  = QP* QT

QED

Proved

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Answer 2

The correct question is In the Fig,PQR and QST are two right triangles ,Right angled at R and T respectively. Prove that QR * QS = QP× QT.

Step-by-step explanation:

Given:

Figure given below in attachment.

ΔPQR,

∠R = 90°

ΔSQT,

∠T = 90°

To Prove That:

QR * QS = QP * QT

Proof:

In ΔPQR and ΔSQT,

∠PQR = ∠SQT   (Common)

∠PRQ = ∠STQ  (Right Angles)

ΔPQR ≈ ΔSQT (By A.A Similarity)

$\frac{QR}{QT} = \frac{OP}{QS} (C.P,S.T)$

Cross Multiplying we get,

QR * QS = OP * QT

Hence Proved