Quadrilaterals

A quadrilateral is a polygon with four sides.

There are many special types of quadrilateral.

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

A parallelogram also has the following properties:

  • Opposite angles are congruent;
  • Opposite sides are congruent;
  • Adjacent angles are supplementary;
  • The diagonals bisect each other.

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.

A rectangle has all the properties of a parallelogram, plus the following:

  • The diagonals are congruent.

 

A rhombus is a parallelogram with four congruent sides. The plural of rhombus is rhombi. (I love that word.)

A rhombus has all the properties of a parallelogram, plus the following:

  • The diagonals intersect at right angles.

A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles.

A trapezoid is a quadrilateral with exactly one pair of parallel sides. (There may be some confusion about this word depending on which country you're in. In India and Britain, they say trapezium; in America, trapezium usually means a quadrilateral with no parallel sides.)

An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent.

A kite is a quadrilateral with exactly two pairs of adjacent congruent sides. (This definition excludes rhombi. Some textbooks say a kite has at least two pairs of adjacent congruent sides, so a rhombus is a special case of a kite.)

A scalene quadrilateral is a four-sided polygon that has no congruent sides. Three examples are shown below.


Venn Diagram of Quadrilateral Classification

The following Venn Diagram shows the inclusions and intersections of the various types of quadrilaterals.