Notes
quadrilateral

Quadrilateral

A quadrilateral is a polygon with four sides.

Types of Quadrilateral

• Square
• Rectangle
• Rhombus
• Parallelogram
• Trapezium
• Kite
• Dart

Interior Angles of a Quadrilateral

Using the formula for the interior angles of a polygon, the interior angles of a quadrilateral add up to $360^\circ$.

Tessellation Properties

A consequence of the fact that the interior angles of a quadrilateral add up to $360^\circ$ is that any quadrilateral will tessellate the plane.

With the vertices of the quadrilateral labelled $A$, $B$, $C$, $D$ as above, the neighbouring quadrilateral along the edge $A B$ is obtained by rotating the quadrilateral by $180^\circ$ and then aligning the edge $B A$ of the rotated along the edge $A B$ of the original. At each vertex this brings one copy of each interior angle and the tessellation then follows from the fact that these angles sum to $360^\circ$.