A quadrilateral is a parallelogram if and only if its diagonals bisect each other (this should be in any geometry book)
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Yes the diagonals of a kite bisect each other at 90 degrees.
No but the diagonals of a square bisect each other at right angles
No.
no
Yes, they do. Also, they are congruent to each other. * * * * * They do bisect each other but they are not congruent.