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

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A parallelogram also has the following properties:

Opposite angles are congruent; Opposite sides are congruent; Adjacent angles are supplementary;

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.

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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.)

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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.

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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.)

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

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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.)

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


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Venn Diagram of Quadrilateral Classification

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