How to prove that a parallelogram is a rhombus
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If you proov that diagonals of a parallelogram are equal in length, that means its a rohombus.
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A rhombus by definition has the following definitions: It is 1) a quadrilateral 2) of equal side lengths 3) in which opposite sides are parallel. A parallelogram is defined as 1) a quadrilateral 2) in which opposite sides are parallel. Therefore, the only thing that differentiates a rhombus from a parallelogram is that a rhombus has equal side lengths. Therefore, to prove that a parallelogram is a rhombus, one just has to prove that condition.
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