Question -
Answer -
Letus consider a right-angled triangle ABC, right-angled at B.
InΔABC,
∠A + ∠B + ∠C= 180° (Angle sum property of a triangle)
∠A + 90º + ∠C = 180°
∠A + ∠C = 90°
Hence,the other two angles have to be acute (i.e., less than 90º).
∴ ∠B is the largest angle inΔABC.
⇒ ∠B > ∠Aand ∠B > ∠C
⇒ AC > BC and AC > AB
[Inany triangle, the side opposite to the larger (greater) angle is longer.]
Therefore,AC is the largest side in ΔABC.
However,AC is the hypotenuse of ΔABC. Therefore, hypotenuse is the longest side in aright-angled triangle.