Question

In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that : PN < RN

Answer 1

In the given ΔPQR,
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)

PN < PR   ....(i)    (∵ PN < PS)
Also,
RT < 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)

RN < PR   .....(ii)  (∵ RN < RT)
Dividing (i) bt (ii),

`"PN"/"RN" < "PR"/"PR"`

`"PN"/"RN" < 1`
PN < RN.