Montessori Geometry: Classification of Quadrilaterals and the Quadrilateral Family Tree

A description of the basic quadrilaterals and how they are related to each other, leading up to the quadrilateral family tree (Montessori quadrilaterals approach)

A quadrilateral is a polygon with four sides.

A trapezoid is a quadrilateral that has at least one pair of parallel sides.

A quadrilateral with no parallel sides is called a common quadrilateral.

A parallelogram is a quadrilateral with two pairs of parallel sides and two pairs of equal-length sides.

Is a parallelogram a trapezoid? Yes, because it has at least one pair of parallel sides.

A rectangle is a quadrilateral with opposite sides that are parallel and equal in length and all four angles are right angles.

Is a rectangle a trapezoid? Yes, because it has at least one pair of parallel sides.

Is a rectangle a parallelogram? Yes, because it has two pairs of parallel sides.

A rectangle is a special kind of parallelogram.

Parallelograms that do not meet the definition of a rectangle are called common parallelograms.

A rhombus is a quadrilateral with equal sides, two pairs of which are parallel.

Is a rhombus a trapezoid? Yes, because it has at least one pair of parallel sides.

Is a rhombus a parallelogram? Yes, because it has two pairs of parallel sides.

Is a rhombus also a rectangle? No, because it does not have all right angles.

A square is a quadrilateral with equal sides, two pairs of which are parallel, and all right angles.

Is a square a trapezoid? Yes, because it has at least one pair of parallel sides.

Is a square a parallelogram? Yes, because it has two pairs of parallel sides.

Is a square a rectangle? Yes, because it has two pairs of parallel sides with all right angles.

Is a square a rhombus? Yes, because it has equal sides, two pairs of which are parallel.