Question -
Answer -
Let us take a line┬аl┬аandfrom point P (i.e., not on line┬аl), draw two line segments PN andPM. Let PN be perpendicular to line┬аl┬аand PM is drawn at someother angle.
In╬ФPNM,
тИаN = 90┬║
тИаP + тИаN + тИаM= 180┬║ (Angle sum property of a triangle)
тИаP + тИаM = 90┬║
Clearly,тИаM is an acute angle.
тИ┤ тИаM < тИаN
тЗТ PN < PM (Side opposite to the smallerangle is smaller)
Similarly, by drawing different linesegments from P to┬аl, 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.