# Geometry Proof : Product of area ofdiagonally opposite triangles in a quadrilateral

The area of a triangle with two sides $a$ and $b$ with included angle $\theta$ is
$\frac{1}{2}ab\sin \theta.$
Call four the four sublengths of the diagonals $a,b,c,d$ and use the above formula four times.
Remember that $\sin (180 - \theta) = \sin \theta.$