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Parallelogram Diagonals Converse
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Statement
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
In simple terms:
If the diagonals cut each other exactly in half, the shape must be a parallelogram.
Example:
In quadrilateral ABCD, if diagonals AC and BD intersect at point E such that AE = CE and BE = DE, then ABCD is a parallelogram.
Why It Matters:
This is a useful test for proving a quadrilateral is a parallelogram when you know something about its diagonals.
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