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Answer :
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.