Question

Two triangles QPR and QSR, right angled at P and S respectively are drawn on the same base QR and on the same side of QR. If PR and SQ intersect at T, prove that PT × TR = ST × TQ

Answer 1

In ∆PQT and ∆STR we have

∠P = ∠S = 90° ...(Given)

∠PTQ = ∠STR ...(Vertically opposite angle)

By AA similarity
∆PTQ ~ ∆STR we get

`"PT"/"ST" = "TQ"/"TR"`

PT × TR = ST × TQ

Hence it is proved.