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A trapezoid with congruent diagonals is an isosceles trapezoid.
There are 2
No, the diagonals of a trapezoid do not necessarily bisect each other. Only in an isosceles trapezoid, where the two non-parallel sides are congruent, will the diagonals bisect each other. In a general trapezoid, the diagonals do not bisect each other.
No.
Not usually.