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

**Solution:**

Let us consider a right-angled triangle ABC, right-angled at B.

In ∆ABC,

∠A + ∠B + ∠C = 180° (Angle sum property of a triangle)

∠A + 90^{o }+ ∠C = 180°

∠A + ∠C = 90°

Hence, the other two angles have to be acute (i.e., less than 90^{o} ).

Thus, ∠B is the largest angle in ∆ABC.

So, ∠B > ∠A and ∠B > ∠C

Therefore, AC > BC and AC > AB [Using theorem 7.7 of triangles, in any triangle, the side opposite to the larger (greater) angle is longer.]

Therefore, AC is the largest side in ∆ABC.

However, AC is the hypotenuse of ∆ABC.

Therefore, the hypotenuse is the longest side in a right-angled triangle.

**Video Solution:**

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

### NCERT Maths Solutions Class 9 - Chapter 7 Exercise 7.4 Question 1:

**Summary:**

Thus, we have proved that in a right-angled triangle, the hypotenuse is the longest side.