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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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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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  1. 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:

    Ncert solutions class 9 chapter 7-27

    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)

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