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.
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.