Question

In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PR > PS

Answer 1

In ΔPQS,
PS ⊥ QR      ....(Given)

PS < PR      ....(Of all the straight lines that can be drawn to a given straight line from a point outside it, the perpendicular is the shortest.)

I.e. PR > PS.