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

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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