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Q: What is a quadrilateral with diagonals that bisect each other?

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A square has two diagonals that bisect each other at 90 degrees

True

There is no quadrilateral on that list with diagonals that bisect each other.

always

true

The missing word is "bisect".

may or may not be

Square, Rhombus

A quadrilateral is a parallelogram if and only if its diagonals bisect each other (this should be in any geometry book)

Square

A quadrilateral whose diagonals bisect each other at right angles is a rhombus. each other at right angles at M. So AB = AD and by the first test above ABCD is a rhombus. 'If the diagonals of a parallelogram are perpendicular, then it is a rhombus

If you are talking about the diagonals of a quadrilateral, the only quadrilateral that have diagonals that are perpendicular and bisect each other is a square, because a rectangle has bisecting diagonals, while a rhombus has perpendicular diagonals. And a square fits in both of these categories.

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