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

**swordfish774** · October 9th 2012, 04:41 AM

In a quadrilateral, product of area of diagonally opposite triangles is same. Can someone please help with a proof. A simple proof would be welcome. Links to proof are also fine.

**BobP** · October 9th 2012, 06:55 AM

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 $\sin (180 - \theta) = \sin \theta.$

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