Flexi Says:
To prove a quadrilateral is a square, we need to show two things: all four sides are equal in length, and all four angles are right angles (90°).
1. All four sides are congruent, i.e., @$\begin{align*}AB = BC = CD = DA\end{align*}@$.
2. All the four angles are congruent and measures @$\begin{align*}90^\circ\end{align*}@$, i.e., @$\begin{align*}\angle ABC\end{align*}@$@$\begin{align*}=\end{align*}@$@$\begin{align*}\angle BCD\end{align*}@$@$\begin{align*} = \end{align*}@$@$\begin{align*}\angle CDA\end{align*}@$@$\begin{align*}=\end{align*}@$@$\begin{align*}\angle DAB\end{align*}@$@$\begin{align*}= 90^\circ\end{align*}@$.
If both conditions are met, then the quadrilateral is a square.
