How i solve the important question of ncert class 9th chapter triangles , What is the best solution of question 6 of exercise 7.4 . Please help me to solve this important question in a easiest and simple way.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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Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest. Q.6
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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
So, AB < AC (As the side opposite to the larger angle is always larger)