A square is a plane geometric figure having 4 equal sides and 4 right angles.
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A quadrilateral with 4 equal sides and 4 right angles is a square.
A square has 4 right angles and 4 equal sides.Its relatives, the rhombus (has 4 equal sides, but not necessarily 4 right angles), the rectangle (4 right angles, but not necessarily 4 equal sides) are the closest as far as quadrilaterals are concerned.
The shape you are looking for is a quadrilateral. If you have a square, all angles MUST be right angles. A parallelogram can also have 4 equal sides in length and parallel sides, but a parallelogram doesn't have right angles.
No. A trapezoid is a 4-sided polygon with one pair of parallel sides. A parallelogram with 4 equal sides is a rhombus. (A parallelogram with 4 equal sides and 4 right angles is a square, which is a special case of a rhombus.)
A rhombus has 4 equal sides but no corner right angles