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Quadrilaterals: Nomenclature

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 reverse sides are parallel .

A parallelogram also has the post-obit properties:

  • Opposite angles are congruent;
  • Contrary sides are congruent;
  • Side by side angles are supplementary;
  • The diagonals bisect each other.

A rectangle is a parallelogram with four correct angles, and so all rectangles are besides 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 honey that word.)

A rhombus has all the properties of a parallelogram, plus the post-obit:

  • The diagonals intersect at right angles.

A foursquare can be defined every bit a rhombus which is too a rectangle – in other words, a parallelogram with four congruent sides and four correct angles.

A trapezoid is a quadrilateral with exactly one pair of parallel sides. (At that place may be some confusion near this give-and-take depending on which state you lot're in. In Republic of india and Britain, they say trapezium ; in America, trapezium unremarkably 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 side by side congruent sides. (This definition excludes rhombi. Some textbooks say a kite has at least two pairs of next congruent sides, then a rhombus is a special case of a kite.)

A scalene quadrilateral is a iv-sided polygon that has no coinciding sides. Three examples are shown beneath.

Venn Diagram of Quadrilateral Classification

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