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

To prove AC is the longest side of ΔABC

Proof:

In ΔABC,

∠A + ∠B + ∠C = 180° [Sum of all angles of a triangle = 180°]

∠A + 90° + ∠C = 180° [Given ∠B = 90°]

∠A + ∠C = 180° - 90°

⸫ ∠A + ∠C = 90°

Hence, ∠A < 90°

∠A < ∠B

BC < AC [Side opposite to a larger angle is longer]

Similarly,

∠C < 90°

∠C < ∠B

AB < AC [Side opposite to a larger angle is longer]

Hence,

⸫ AC is the longest side of ΔABC i.e. the hypotenuse.