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Math Question

9 In parallelogram \( A B C D \), diagonals \( \overline{A C} \) and \( \overline{B D} \) intersect at \( E \). Which statement does not prove parallelogram \( A B C D \) is a rhombus?
(1) \( \overline{A C} \cong \overline{D B} \)
(2) \( \overline{A B} \cong \overline{B C} \)
(3) \( \overline{A C} \perp \overline{D B} \)
(4) \( \overline{A C} \) bisects \( \angle D C B \).

Solution

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