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

Given: x is a line and A is a point not lying on x.

C is any point on x other than B.

To prove: AB < AC
Proof:
In $$\triangle{ABC}$$, $$\angle{B}$$ is the right angle.

Therefore, $$\angle{C}$$ is an acute angle.
$$\Rightarrow$$ $$\angle{C}$$ < $$\angle{B}$$
$$\therefore$$ AB < AC
(Since, side opposite to greater angle is longer)

Hence, proved that the perpendicular line segment is the shortest.