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

To do:

We have to show that in a right-angled triangle, the hypotenuse is the longest side.

Solution:

Let us consider $ABC$ a right-angled triangle

We know that the sum of the interior angles of the triangle is always $180^o$.

This implies,

$\angle A+\angle B+\angle C=180^o$

$90^o+\angle B+\angle C=180^o$

$\angle B+\angle C=180^o-90^o$

$\angle B+\angle C=90^o$

Now, we have

$\angle B+\angle C=\angle A=90^o$

From this, it is clear that $\angle A$ is the largest angle.

We know that the side opposite the largest angle is the longest side.

This implies,

$AB$ is the longest side.

Therefore,

$AB$ is the hypotenuse of the $\triangle ABC$ and is the longest side of $\triangle ABC$.

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Updated on: 10-Oct-2022

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