Prove that, of all line segments that can be drawn to a given line, from a point, not lying on it, the perpendicular line segment is the shortest
It is given in the question that,
l is the straight line and A is a point that is not lying on l
AB is perpendicular to line l and C is the point on l
As, ∠ B = 90o
So in ∆ABC, we have:
∠ A + ∠ B + ∠ C = 180o
∠ A + ∠ B = 90o
∴ ∠ C < 90o
∠ C < ∠ B
AB < AC
As C is that point which can lie anywhere on l
∴ AB is the shortest line segment drawn from A to l
Hence, proved
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