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Prove that the sum of the squares of th...

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Text Solution

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Let ABCD be rhombus with O as diagonals intersection point.
In `/_\AOB`,
Using pythagoras theorem,
`AB^2 = AO^2 + OB^2`
Similarly,
`BC^2 = OC^2 + OB^2`
`DC^2 = OD^2 + OC^2`
`DA^2 = DO^2 + OA^2`
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