How about a tall, skinny kite ? The top 2 sides are equal, and the bottom 2 sides
that come together where the tail attaches are equal. It's not a paralleogram,
because the equal sides are adjacent, not opposite and parallel.
Also, how about a weird irregular pentagon, or a weird irregular hexagon, with
2 pairs of equal sides, and the other 1 or 2 sides being any old size you want.
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A rectangle is defined as any shape with two pairs of equal sides and four equal angles.
rectangle
a parallelogram
A parallelogram is such a shape.
A square has 4 right angles, and 2 pairs of equal, perpendicular sides.