Yes. It would be a rhombus.
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rhombus
A rectangle and a square are two types of quadrilaterals having four equal angles, where each of them equals a right angle.
No, a quadrilateral with congruent diagonals but no right angles is not necessarily a parallelogram. In order for a quadrilateral to be classified as a parallelogram, it must have both pairs of opposite sides parallel. The property of having congruent diagonals does not guarantee that the sides are parallel, so the quadrilateral may not be a parallelogram.
Congruent.
A parallelogram.