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What has 4 equal sides its opposite sides are parallel and its angles may be right angles?
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.
A parallelogram with four equal sides but no right angles?
it is a rhombus
Is a trapezoid a parallelogram with 4 equal sides but no 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 parallelogram with 4 right angles and with sides different in length and width?
Well, honey, that's not a parallelogram, that's a rectangle. A parallelogram can have opposite sides equal in length and opposite angles equal in measure, but not necessarily right angles. So, in this case, you're describing a rectangle, not a parallelogram. But hey, at least you're on the right track!
What shape has 2 pairs of equal sides and no right angles?
A shape that has 2 pairs of equal sides and no right angles is a kite or a parallelogram. In a parallelogram, each side is equal to the one directly opposite; in a kite, the equal sides are adjacent to one another.
