Question

if RS and PT are altitudes of a triangle PQR. prove that (1). triangle PQT is similar to triangle QRS (2). PQ*QS=RQ*QT

Answer 1

hey here is your solution

Answer 2

Altitudes of ΔPQR = RS and PT

1. In ΔPQT and ΔQRS,

∠PTQ = ∠RSQ = 90° (Given)

∠PQT = ∠RQS (Common angle)

ΔPQT ~ Δ RQS (By similarity AA)

2. Since ΔPQT and ΔRQS are similar

Thus,

PQ/RQ = QT/QS

= PQ × QS = RQ × QT

Hence proved