There are infinitely many polygons which have this property. The easiest to think of is a right triangle. But there are also quadrilaterals, pentagons, etc., that can be constructed that have this property.
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shape no pairs of perpendicular sides
Trapezium
No. By definition, a rectangle must have TWO pairs of parallel sides. Also, each pair of parallel sides will be congruent. *If this is not happening with your shape, it isn't a rectangle.
A trapezium or parallelogram. A pentagon can have a pair of parallel sides. Polygons with 6 or more sides can have two (or more) pairs of parallel sides.
A trapezoid.
shape no pairs of perpendicular sides
Trapizium
trapazoid
trapezoid
I think this person means the trapazoid. It has only one pair of parallel sides.
It could be a right angle triangle
It fits the description of a right angle triangle
Any shape wit four of more sides can have one pair of parallel sides.
The only requirement for a trapezoid is that one pair of opposite sides be parallel. There could be trapezoids with a pair of perpendicular lines.
Any polygon with four or more sides can have a pair of parallel sides. It is also possible to to have non-polygonal shapes - eg a cigar-shape - that has parallel sides.
The first geometric shape that comes to mind with no perpendicular sides is a triangle.
A trapezium is a shape with four sides. Of these, one pair of sides are parallel. The only restriction on the other pair is that they are not parallel (because you then have a parallelogram).