Question

In ∆ABC, if ∠A = ∠B = 45° name the longest side.

Answer 1

In$∆ABC$, we have:
$\angle A=\angle B=45°\left(\mathrm{Given}\right)$

$$\begin{gathered} \mathrm{Further},\angle A+\angle B+\angle C=180° \\ \Rightarrow 45°+45°+\angle C=180° \\ \Rightarrow \angle C=180°-45°-45°=90° \end{gathered}$$

Thus, the side opposite to $\angle C$, i.e., AB, is the longest side.

The side AB is the hypotenuse of triangle ABC.