square, rectangle and an isosceles trapezoid
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A trapezoid with congruent diagonals is an isosceles trapezoid.
Only the diagonals of isosceles trapezoids are congruent.
No not normally only if the parallelogram is in the form of a rectangle will it then have congruent diagonals.
No, the diagonals of a rhombus are not congruent, but they do intersect each other at 90 degrees.
No. The diagonals of a parallelogram are congruent if and only if the parallelogram is a rectangle.