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

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To prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals, we will follow these steps: ### Step-by-Step Solution: 1. **Understanding the Rhombus:** A rhombus has four equal sides. Let the length of each side be \( A \). Therefore, the sum of the squares of the sides is: \[ \text{Sum of squares of sides} = A^2 + A^2 + A^2 + A^2 = 4A^2 ...
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