Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
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12/07/2021 12:33 pm
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Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
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12/07/2021 12:34 pm
First, let “l” be a line segment and “B” be a point lying on it. A line AB perpendicular to l is now drawn. Also, let C be any other point on l.
The diagram will be as follows:
To prove:
AB < AC
Proof:
In ΔABC, B = 90°
Now, we know that
A+B+C = 180°
∴ A +C = 90°
Hence, C must be an acute angle which implies C < B
AB < AC (As the side opposite to the larger angle is always larger)
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