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

Posted by Nisha Butar 5 years, 7 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 7 months ago

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

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