A *quadrilateral* is a two-dimensional shape made of four straight lines that connect in four *vertices*, or corners. Quadrilaterals go by different names, depending on the size of their angles and the properties of their sides. **Squares, parallelograms, and trapezoids are all common forms of quadrilaterals.**

## Squares and Rectangles

*Squares* are one of the most familiar forms of quadrilaterals. **A square has four sides of equal length.** In addition, each of a square's four corners is a 90-degree angle. Opposite sides of a square are parallel to each other.

Like a square, **a rectangle's opposite sides are parallel, and its corners are all 90-degree angles.** However, not all of a rectangle's sides are of equal length. Any two opposite sides of a rectangle are equal, but two neighboring, or

*adjacent*, sides of a rectangle have different lengths.

## Rhombuses and Parallelograms

Diamond-shaped *rhombuses* have a great deal in common with squares -- **all four of a rhombus's sides have equal length, and its opposite sides are parallel to each other.** However, there is one important difference. None of a rhombus's angles are 90 degrees. Any two opposite corners of a rhombus have equal angles.

A *parallelogram* is to a rectangle as a rhombus is to a square. As the name suggests, **opposite sides of a parallelogram are parallel to each other.** Opposite sides also have equal lengths; however, the adjacent sides of a parallelogram have unequal lengths. Like a rhombus, any two opposite corners of a parallelogram have equal angles.

## Trapezoids and Kites

Not all quadrilaterals are completely parallel. **A trapezoid has only one pair of parallel sides, which are of unequal length.** The other two sides of a trapezoid are not parallel, though they may be of equal length.

A *kite* has no parallel sides. Instead, **a kite has two pairs of sides with equal length.** The equal sides of a kite are adjacent to each other, rather than opposite from each other. The two corners where the kite's unequal lines meet are opposite each other, and are equal angles.

## Complex Quadrilaterals

What is a *complex quadrilateral*? A complex quadrilateral is a quadrilateral where two lines end up crossing over one another. Imagine taking a square and twisting its top around so its two side edges cross each other. The shape you'll create looks like two triangles with their tips touching. Because of this, **complex quadrilaterals are sometimes called butterfly quadrilaterals or crossed quadrilaterals.**

Complex quadrilaterals have different rules regarding angles than other quadrilaterals. **The four angles of most quadrilaterals add up to 360 degrees.** However, two of a complex quadrilateral's angles measure around the outside of the corners, rather than the inside -- and the four angles of a complex quadrilateral add up to 720 degrees.