Overview: What Are Quadrilaterals?
Quadrilaterals are polygons with four sides. They are classified according to measures of equal angles and equal sides. There are seven different types of quadrilaterals: parallelogram, rhombus, rectangle, square, kite, trapezoid, and isosceles trapezoid. Types of quadrilaterals often overlap, so that a figure that fits in one category may also fit in another. Each has its own special features.
Definitions
A quadrilateral is a parallelogram if both pairs of its opposite sides are parallel. A rhombus is a type of quadrilateral with all sides the same length. A rectangle has 4 right angles, and a square has four equal sides and four right angles. These definitions exist in a hierarchy of relationships. For example, every square is also a parallelogram, because both pairs of its opposite sides are equal, but every parallelogram is not a square. Similarly, every square is also a rhombus, because all four sides are the same length, but every rhombus is not a square. Likewise, every square is also a rectangle, because a rectangle has 4 right angles, but every rectangle is not a square.
Kites
Kites are a special type of quadrilateral with two distinct pairs of consecutive sides the same length. Because rhombi and squares also have sides the same length, they are also kites, but the reverse is not true. Every kite is not a rhombus, because all sides of a kite are not equal. Similarly, every kite is not a parallelogram, because the opposite sides of a kite are not necessarily parallel.
Trapezoids
Trapezoids are quadrilaterals that have one pair of parallel sides. The parallel sides are called bases. If the base angles are equal, the trapezoid is a special type called an isosceles trapezoid. Rectangles are a special type of isosceles trapezoid with opposite sides parallel and equal angles.
Diagonals
Quadrilaterals have two diagonal lines. In a kite, the diagonal joining the ends forms a line of symmetry. In a rhombus, both diagonals form lines of symmetry. Lines of symmetry hold powerful properties that help measure angles, area, and relationships between geometric figures.
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