Question -
Answer -
Let us take a line l andfrom point P (i.e., not on line l), draw two line segments PN andPM. Let PN be perpendicular to line l and PM is drawn at someother angle.
InΔPNM,
∠N = 90º
∠P + ∠N + ∠M= 180º (Angle sum property of a triangle)
∠P + ∠M = 90º
Clearly,∠M is an acute angle.
∴ ∠M < ∠N
⇒ PN < PM (Side opposite to the smallerangle is smaller)
Similarly, by drawing different linesegments from P to l, it can be proved that PN is smaller incomparison to them.
Therefore,it can be observed that of all line segments drawn from a given point not onit, the perpendicular line segment is the shortest.