A quadrilateral is a _________ if and only if the sum of the squares of its sides is equal to the sum of the squares of its diagonals. Prove it.
If a quadrilateral verifies that property then the middle points of both diagonals are a single point (applaying Euler's theorem for quadrilaterals), and this implies that it is a paralelogram.
Euler:
D^2+d^2 = a^2+b^2+c^2+d^2+4MN
where MN is the segment uniting the middle points of both diagonals.
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Also for the theorem of cosine it is very easy to show that each paralalogram verifies that property.

Posted by armando
on 20180127 09:50:42 