Kite properties

Dependencies: SSS congruence, Isoceles: median, altitude, bisector coincide.

Statement

Let the quadrilateral $ABCD$ satisfy the two pairs of equal adjacent sides:

Such a quadrilateral is called a kite, with $AC$ its axis diagonal (joining the two common vertices $A$, $C$ of the adjacent-side pairs) and $BD$ its cross diagonal. Then

where $P = AC \cap BD$. In other words, the diagonal $AC$ is the perpendicular bisector of $BD$, and it bisects the apex angles $\angle BAD$ and $\angle BCD$.