Question

Give a geometrical interpretation of the parallelogram identity.

Answer 1

I'm not sure about geometrical, but it looks a lot like 2 Pythagoras' theorems stuck together. but as the angles are not always 90 degrees, the cosine rule, the pimped up Pythagoras' theorem, can be used.

\[p^2=x^2+y^2-2xycos ( 180-\alpha)\]
\[q^2=x^2+y^2-2xycos ( \alpha)\]
\[p^2+q^2=2x^2+2y^2\]