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Not necessarily - the diagonals of a rhombus bisect each other (they are perpendicular bisectors of each other), but are not equal.

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Q: Are diagonals congruent if they bisect each other?
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Do the diagonals of a parallelogram bisect each other?

Yes, they do. Also, they are congruent to each other. * * * * * They do bisect each other but they are not congruent.


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