SOLUTION: prove the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Question 420398: prove the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose we have a rhombus, with diagonals AC and BD intersecting at E.

Let AE = EC = x, BE = ED = y, and AB = z. The diagonals of a rhombus are perpendicular, so . The sum of the squares of the diagonals is given by . This is equal to , which is also equal to the sum of the squares of the side lengths (since each side has length ).
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