Question

prove that hypotenuse is the largest side of any right angle triangle ​

Answer 1

solution

In the given triangleABC,

Angle B = 90°

Hence Angle A + Angle C = 180°-90°.....[Sum of all angles of the triangle are 180°.]

Therefore Angle B is the greater angle than Angle A and Angle C. [Angle A>Angle C ]

We know that.. Side opposite to greater angle is always longer.

Therefore.. Side opposite to angle B is AC

[AC > BC and AC > AB]

That is AC is the longest side..

[AC is the hypotenuse]

_____________________________

This is the answer.

Answer 2

Let ABC be a ∆ right angled at B.

Now ,

<A +<B +<C = 180

<A + 90+ <C =180

<A + <C =90

→<A + <C = <B.

Since , whole is always greater than its parts

→<B ><A

and , <C><A.

Now , side opposite to greater angle is larger .

→AC>AB and BC.

Thus , hypotenuse is the longest side in a right angled ∆.