Quadrilaterals

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners.

Types of Quadrilaterals

1. Square: A quadrilateral with all sides equal in length and all angles equal to 90 degrees.
2. Rectangle: A quadrilateral with opposite sides equal in length and all angles equal to 90 degrees.
3. Rhombus: A quadrilateral with all sides equal in length, but not all angles are 90 degrees.
4. Parallelogram: A quadrilateral with opposite sides equal in length and opposite angles equal. The opposite sides are parallel.
5. Trapezoid (US) / Trapezium (UK): A quadrilateral with one pair of opposite sides parallel.
6. Trapezium (US) / Trapezoid (UK): A quadrilateral with no parallel sides.
7. Kite: A quadrilateral with two pairs of adjacent sides that are equal in length.

Properties of Quadrilaterals

1. Sum of Angles: The sum of the interior angles in any quadrilateral is 360 degrees.
2. Diagonals: The diagonals of a quadrilateral have special properties depending on the type of quadrilateral. For instance, in a rectangle, the diagonals are equal in length, while in a rhombus, they are perpendicular bisectors of each other.

Applications

Quadrilaterals are used extensively in various fields including geometry, architecture, design, engineering, and more. They are also the simplest polygonal shape used in meshing for computer graphics and finite element analysis.