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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 opposite sides are parallel .

A parallelogram also has the post-obit properties:

  • Reverse angles are coinciding;
  • 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, non 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 beloved that word.)

A rhomb has all the backdrop of a parallelogram, plus the following:

  • The diagonals intersect at right angles.

A square can exist defined as a rhomb which is also a rectangle – in other words, a parallelogram with iv 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 discussion depending on which state 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 coinciding.

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

A scalene quadrilateral is a 4-sided polygon that has no congruent sides. Iii examples are shown below.

Venn Diagram of Quadrilateral Classification

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