If ABCD is a rectangle and P is any point its interior, prove" AP˛+PC˛ =PB˛+PD˛
draw a rectangle and label the corners ABCD.
Pick any point in the interior, label it P.
Join P to all 4 corners by drawing lines and also draw the vertical lines (parallel to the 2 vertical sides) from P to the base and top of the rectangle.
Now you can use Pythagoras' theorem on the 4 resulting right-angled triangles.