Quadrilaterals are polygons with four sides and four corners or angles. The word root quad- has the meaning of four. The quadrilateral family has several different names for each type of quadrilateral. However, quadrilaterals can be broken down into two categories: parallelograms or trapezoids. A trapezoid does not have any related figures. It can simply be called a trapezoid, as an exact name or a quadrilateral. The second category is parallelograms. There are several subtypes of parallelograms. In fact, the square, rectangle and rhombus can all also be classified as a parallelogram. Hence, all quadrilaterals have at lease two ways to be classified. However, some will have more. For example, the square can be classified as a rectangle, a rhombus, a parallelogram, a quadrilateral, or the most exact name, a square. The description below can be used to find the most exact name for a quadrilateral.
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
A rhombus is a parallelogram that has all sides congruent.
A rectangle is a parallelogram with four right angles.
A square is a rectangle, rhombus and parallelogram with all sides congruent. Looking at the descriptions above, we can understand why a square has so many names. A square is a quadrilateral because it has four sides and four corners. A square can also be classified as a parallelogram because both pairs of its opposite sides are parallel. A square can be classified as a rhombus because it is a parallelogram with all sides congruent. Finally, a square can be classified as a rectangle because it is a parallelogram with four right angles.
Though quadrilaterals can be classified in many ways, it is best to always label a quadrilateral with its most exact name, unless asked to do otherwise.