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