The answer depends on which shape you’re looking at. A parallelogram has two pairs of parallel opposite sides. A trapezoid has just one pair. Some shapes, like kites and irregular quadrilaterals, have zero. And once you move beyond four-sided shapes, the number of parallel pairs keeps growing.
This question comes up most often with quadrilaterals (four-sided shapes), so let’s start there and then look at what happens with larger polygons.
Shapes With Two Pairs of Parallel Sides
A parallelogram is defined as a quadrilateral with two pairs of parallel sides. Each side runs parallel to the one directly opposite it. This is the defining feature of the shape, and several familiar shapes fall into this family.
A rectangle has two pairs of parallel opposite sides, plus four right angles. A square has two pairs of parallel opposite sides, four right angles, and four equal-length sides. A rhombus has two pairs of parallel opposite sides and four equal-length sides, but its angles don’t have to be 90 degrees. All three are special types of parallelograms, so they all share that core property: two pairs of parallel sides.
Shapes With One Pair of Parallel Sides
A trapezoid has exactly one pair of parallel sides. Those two parallel sides are called the bases, while the other two sides (which angle toward or away from each other) are called the legs. In the United States, “trapezoid” is the standard term. In the UK, Australia, and most other English-speaking countries, the same shape is called a trapezium.
There’s a small debate in math education about whether “trapezoid” means exactly one pair or at least one pair of parallel sides. Under the exclusive definition, a trapezoid has one and only one pair, which means parallelograms don’t count as trapezoids. Under the inclusive definition, any quadrilateral with at least one pair of parallel sides qualifies, so parallelograms are technically trapezoids too. Most modern geometry textbooks use the inclusive definition, but your class may use either one.
Shapes With Zero Parallel Sides
A kite has no pairs of parallel sides at all. Its two pairs of consecutive sides are equal in length, but opposite sides aren’t parallel. The same goes for a general irregular quadrilateral where no two sides happen to line up in the same direction.
Regular Polygons With More Than Four Sides
Once you move past quadrilaterals, the rule for regular polygons (shapes where all sides and angles are equal) is straightforward. If the polygon has an even number of sides, every side has an opposite side that runs parallel to it. The number of parallel pairs equals half the number of sides.
- Regular hexagon (6 sides): 3 pairs of parallel opposite sides
- Regular octagon (8 sides): 4 pairs of parallel opposite sides
- Regular decagon (10 sides): 5 pairs of parallel opposite sides
In a regular octagon, for example, if you number the sides 1 through 8 going around, side 1 is parallel to side 5, side 2 is parallel to side 6, side 3 is parallel to side 7, and side 4 is parallel to side 8.
What About Odd-Sided Polygons?
Regular polygons with an odd number of sides, like pentagons and heptagons, don’t have any opposite sides at all. Each side faces a vertex (corner) rather than another side. So a regular pentagon has zero pairs of parallel opposite sides. That said, a regular pentagon does contain parallel lines in a different sense: each diagonal is parallel to one of the sides. But when the question is specifically about opposite sides, the answer for odd-sided polygons is zero.
Quick Reference by Shape
- Square: 2 pairs
- Rectangle: 2 pairs
- Rhombus: 2 pairs
- Parallelogram: 2 pairs
- Trapezoid: 1 pair
- Kite: 0 pairs
- Regular hexagon: 3 pairs
- Regular octagon: 4 pairs
- Regular pentagon: 0 pairs (no opposite sides exist)