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Show that in a right angled …

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Show that in a right angled triangle, the hypotenuse is the longest side.

    • Posted by Nisha Butar 5 years, 1 month ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Sia ? 5 years, 1 month ago


    Let {tex}\triangle{/tex}ABC be a right angled triangle in which {tex}\therefore{/tex}B = 90o
    Then {tex}\angle{/tex}A + {tex}\angle{/tex}C = 90o . . . .[sum of three angles of a triangle]
    {tex}\therefore{/tex} {tex}\angle{/tex}B = {tex}\angle{/tex}A + {tex}\angle{/tex}C
    {tex}\therefore{/tex} {tex}\angle{/tex}B > {tex}\angle{/tex}A
    and {tex}\angle{/tex}B > {tex}\angle{/tex}C
    {tex}\therefore{/tex} AC > BC . . . [Side opposite to greater angle is longer]
    and AC > AB
    {tex}\therefore{/tex}  AC is the longest side, i.e. hypotenuse is the longest side.

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