Question

In the figure, RQ perpendicular to PQ, PQ perpendicular to PT and ST perpendicular to PR. Prove that: ST×QR = PS×PQ​

Answer 1

Given:

RQ ⊥ PQ, PQ ⊥ PT, ST ⊥ PR

To prove:

ST · QR = PS · PQ

Proof:

In Δ PQR and Δ PST

∠ R = ∠ R [common angle]

∠ S = ∠ R [90°]

∴ \triangle QR \sim \triangle PST△QR∼△PST

⇒ \frac{ST}{PQ}= \frac{PS}{RQ}

PQ

ST

=

RQ

PS

⇒ ST · QR = PS · PQ

Hence proved.