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

Answers (1)

Consider a right-angled triangle ABC with right angle at B.

Then              \angle B\ >\ \angle A\ or\ \angle C            (Since \angle B\ =\ 90^{\circ})

Thus the side opposite to largest angle is also largest.        AC\ >\ BC\ or\ AB

Hence the given statement is proved that all line segments are drawn from a given point, not on it, the perpendicular line segment is the shortest.

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