Rectangle.
If all of the angles are equal to each other (360/4), each one is 90 degrees, or a right angle. If two pairs are equal to each other and each angle is 90 degrees, the shape is a rectangle. It could also be a square, a type of rectangle, if all of the sides are the same length. NOTE: All squares are rectangles, but not all rectangles are squares.
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A kite.
An isosceles trapezium.
A 'KITE' ; two adjacent sides may be of equal length. A parallelogram has two pairs of equal and parallel sides.
A rhombus. Commonly referred to as a "diamond".
Diagonally opposite pairs of angles will always be equal, but the only time all angles in a quadrilateral parallelogram are equal is when that shape is a rectangle.