GKT101: General Knowledge for Teachers – Math

A kite is a convex quadrilateral with two pairs of adjacent congruent sides such that not all sides are congruent.

The angles between the congruent sides are called vertex angles. The other angles are called non-vertex angles.

The Properties of a Kite:

1. Two pairs of adjacent sides are congruent, i.e., $\begin{align*}AB = AD\end{align*}$ and $\begin{align*}BC = CD\end{align*}$.

2. Non-vertex angles are congruent, i.e., $\begin{align*}\angle{ABC} = \angle{ADC}\end{align*}$.

3. Diagonals intersect 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*}$.

4. The longer diagonal of a kite bisects the shorter one, i.e., $\begin{align*}BO = OD\end{align*}$.

5. The diagonal through the vertex angles is the angle bisector for both angles, i.e., $\begin{align*}\angle{BAC} = \angle{DAC}\end{align*}$ and $\begin{align*}\angle{BCA} = \angle{DCA}\end{align*}$.

6. One of the diagonals bisects the kite, i.e., divides it into two congruent triangles, i.e., $\begin{align*}\triangle ABC \cong \triangle ADC\end{align*}$.