Square

A square is a quadrilateral with four right angles and four congruent sides. All squares are rectangles and rhombuses.

 

The Properties of a Square:

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., \(\begin{align*}\angle ABC\end{align*}\)\(\begin{align*}=\end{align*}\)\(\begin{align*}\angle BCD\end{align*}\)\(\begin{align*} = \end{align*}\)\(\begin{align*}\angle CDA\end{align*}\)\(\begin{align*}=\end{align*}\)\(\begin{align*}\angle DAB\end{align*}\)\(\begin{align*}= 90^\circ\end{align*}\).

3. Diagonals are congruent, i.e., \(\begin{align*}AC = BD\end{align*}\).

4. Diagonals bisect each other at right angles, i.e., \(\begin{align*}\angle AOB\end{align*}\)\(\begin{align*}=\end{align*}\)\(\begin{align*}\angle BOC\end{align*}\)\(\begin{align*}=\end{align*}\)\(\begin{align*}\angle COD\end{align*}\)\(\begin{align*}=\end{align*}\)\(\begin{align*}\angle DOA\end{align*}\)\(\begin{align*}= 90^\circ\end{align*}\).

All the angles of a quadrilateral are congruent and make right angles. What type of quadrilateral is this?


All the angles of a _______ (kite/trapezoid/rectangle) are congruent and make right angles.