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

Posted by Nisha Butar 6 years, 2 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 2 months ago

Let {tex}\triangle{/tex}ABC be a right angled triangle in which {tex}\therefore{/tex}B = 90^o
Then {tex}\angle{/tex}A + {tex}\angle{/tex}C = 90^o . . . .[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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