Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

Given: FB is a line and A is a Point Outside of FB.
To Prove: AB is smallest line segment.
In ΔABC, ∠B = 90° [∵ Given]
Therefore, ∠BAC <90° and ∠ACB ∠ACB [∵ ∠B = 90° and ∠ACB AB [∵ In a triangle, Greater angle has Longer side opposite to it] Similarly, AD > AB, AE > AB and AF > AB,
Hence, AB is the Smallest line.