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If diagonals bisect each other, opposite sides of quadrilateral are equal and it would be a parallelogram. But then diagonals may not be congruent. If they are congruent, then it must be a rectangle.
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Isosceles trapezoid.
Isosceles trapezoid is a quadrilateral whose diagonals are congruent (equal in length) but they do not bisect each other.
Other characteristics of an isosceles trapezoid are:
- Two opposite sides (it's bases) are parallel.
- Two other sides (it's legs) are equal in length.
- The diagonals are of equal length but they never bisect each other.
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