Q: What is a polygon with 4 sides and no pair of parallel sides?

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A polygon with 4 or more sides can have a pair of parallel sides.

quadrilateral

rhombus

A trapezoid.

For a 4-sided polygon (a quadrilateral), the shape is a trapezoid (trapezium in the UK).*The question was copied in and omitted the "4 sided" restriction. There are innumerable irregular polygons that have a single pair of parallel sides, those that have 5 or more sides.

An irregular quadrilateral, though it could possibly be a kite if there are two pairs of sides of equal length

I am a quadrilateral, I have 4 vertices, I only have one pair of parallel sides, and I am also a polygon. What am I?

Any polygon with 4 or more sides can have 2 parallel sides.

Any irregular polygon with 4 or more sides can have only one pair of parallel sides. For example, a child's drawing of the silhouette of a house (the base, two walls and a triangular roof) is a pentagon and the two walls are the 1 pair of parallel sides.

trapazoid

quadrilateral

There are two pairs of parallel sides in a rectangle - 1 pair of lengths, and 1 pair of widths.Therefore, 4 parallel sides!