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

Answers (1)

Consider a right-angled triangle ABC with right angle at A.

We know that the sum of interior angles of a triangle is 180.

So,                                    \angle A\ +\ \angle B\ +\ \angle C\ =\ 180^{\circ}

or                                       90^{\circ}\ +\ \angle B\ +\ \angle C\ =\ 180^{\circ}

or                                                       \angle B\ +\ \angle C\ =\ 90^{\circ}

Hence \angle B and \angle C are less than \angle A   (90^{\circ}).

Also, the side opposite to the largest angle is also the largest.

Hence the side BC is largest is the hypotenuse of the \Delta ABC.

Hence it is proved that in a right-angled triangle, the hypotenuse is the longest side.

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