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

. AP is perpendicular line segment on line l and AQ is any other line segment. A L APQ > L AQP [In a triangle, if an angle is 90°, other two angles are less than 90°.] < P a > / => AQ > AP. Hence, any line segment AQ, from point A to the line l, is greater than the perpendicular line segment AP, from point A to the line l. Hence, AP is the shortest segment of all the segments.