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

(N/A) Let us consider a point $P$ not on line $l$. Let $PM$ be the perpendicular from $P$ to line $l$,and let $N$ be any other point on line $l$ such that $N \neq M$.
In $\Delta PMN$,since $\angle M = 90^o$,the sum of angles is $\angle M + \angle N + \angle P = 180^o$.
This implies $\angle N + \angle P = 90^o$,so $\angle N < 90^o$.
Since $\angle N < \angle M$,the side opposite to $\angle N$ must be smaller than the side opposite to $\angle M$.
Therefore,$PM < PN$.
Since $N$ is an arbitrary point on line $l$ (other than $M$),this shows that $PM$ is shorter than any other line segment drawn from $P$ to line $l$.
Thus,the perpendicular segment is the shortest line segment drawn from a point to a line.