Question

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

Answer 1

Given,
∆ABC is a right angled triangle
, right - angled at B i.e. ∠B = 90°

To prove : AC is the longest side of ∆ABC.

Prove:
In ∆ABC ,
∠A +∠B +∠C =180 ( Angle Sum Property)
∠A + 90° +∠C = 180
∠A +∠C = 180-90
∠A +∠C = 90
Angle can not be 0 or negative.

Answer 2

In the given triangle ABC,

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]