Question

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

Answer 1

In ΔPQS, 

PS < PQ    ....(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. PQ > PS

Also, QS < QP   ....(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. PQ > QS.