Look around you! Many objects in daily life such as a book, window, television screen, or floor tile have four sides.
Shapes like these are examples of quadrilaterals.
Definition
A quadrilateral is a four-sided closed two-dimensional shape. It has four sides, four vertices, and four angles.
The word quadrilateral comes from “quad” (four) and “lateral” (sides), so it means a four-sided polygon.
In a quadrilateral,
- The four sides meet at four points called vertices.
- The sides form four angles at these vertices.
- The line segments that join opposite vertices are called diagonals.
Example:
In a quadrilateral \(ABCD\),
\(AB, BC, CD\) and \(DA\) are the four sides.
\(A, B, C,\) and \(D\) are the vertices.
\(\angle A, \angle B, \angle C\) and \(\angle D\) are the interior angles.
\(AC\) and \(BD\) are the diagonals.
Important!
In a quadrilateral, the sum of its interior angles is \(360^\circ\).
Quadrilaterals can have different shapes depending on the lengths of their sides and the measures of their angles.
Some special types of quadrilaterals that you will study in this chapter are parallelogram, rectangle, square, rhombus, trapezium, and kite.