Classifying two-dimensional shapes

Different categories of quadrilaterals - part 1

The most important set of quadrilaterals is the set of parallelograms, that is, those with two pairs of opposite sides parallel.

Two lines drawn in a two-dimensional plane are said to be parallel if theoretically they would never meet if continued indefinitely. This describes the relationship between the opposite sides in each of the shapes drawn. Not all parallelograms have reflective symmetry: only some parallelograms have reflective symmetry. But they do all have rotational symmetry of order two or four. This means that the opposite angles match on to each other, and the opposite sides match on to each other, when the shape is rotated through a half-turn. In other words, the opposite angles in a parallelogram are always equal and the opposite sides are always equal. There are then two main ways of classifying parallelograms. One of these is based on the angles, the other on the sides.