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Show that of all line segments …

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Show that of all line segments drawn from a given point not on it,rhe perpendicular line segment is the shortest

    • Posted by Bisla Chingkheimayum 3 years, 7 months ago

    CBSE > Class 09 > Mathematics
    • 2 answers

    Harpreet Singh 3 years, 7 months ago

    Thank you ?

    1Thank You

    Amanjot Kaur 3 years, 7 months ago

    We have a straight line  AB. Take a point P not on AB, but some distance away.  We draw PC the perpendicular on to AB meeting AB at C.  We draw another line from P to D, where D lies on AB.  We show that PD > PC, for any point D other than C. In the triangle PCD, use the Pythagorean law for sides: PC² + CD² = DP² Since CD² is positive and adds to PC²,    PC²+CD² > PC² Hence DP² > PC² So  DP > PC SO PC, the perpendicular distance from an external point to a line segment, is the shortest.

    4Thank You

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