A quadrilateral is a polygon with four sides, four vertices, and four angles. It is one of the most basic shapes in geometry. They may be seen everywhere in our daily lives. The sum of all the interior angles of any given quadrilateral is always equal to 360 degrees. It has various shapes and forms. Let’s understand these in detail.
A quadrilateral is any shape that has four sides. The word comes from “quad,” meaning four, and “lateral,” meaning side. All quadrilaterals have the following features:
The classification of quadrilaterals depends on the length of their sides and the size of their angles. Based on these properties, quadrilaterals can be divided into several types.
Let’s look at a table that summarises this classification:
Let’s now explore each type in detail.
A parallelogram is a quadrilateral where the opposite sides are equal in length and parallel. It looks like a slanted rectangle.
A rectangle is a special type of parallelogram. It has all the features of a parallelogram but with four right angles.
A square is a specific type of rectangle with all four sides equal in length. It is both a rectangle and a rhombus.
A rhombus is a specific quadrilateral where all sides are equal, but the angles are not necessarily 90 degrees. It looks like a diamond.
A trapezium has only one pair of opposite sides parallel. It does not have equal sides or equal angles.
A kite is a geometric quadrilateral with two pairs of adjacent sides of equal length. It looks like a traditional flying kite.
Special quadrilaterals are those with unique properties. These include:
These shapes are important in geometry, architecture, and daily life.
Let’s take a closer look at the properties of quadrilaterals as a whole:
All quadrilaterals have four sides. The sides may be equal or unequal.
All quadrilaterals have four angles. The sum of all interior angles in any quadrilateral is always 360 degrees.
Quadrilaterals have two diagonals that connect opposite corners. The behaviour of diagonals depends on the type of quadrilateral.
Some quadrilaterals, like squares and rectangles, have lines of symmetry. Kites and rhombuses also show symmetrical properties.
Parallelograms, rectangles, rhombuses, and squares have two pairs of parallel sides. Trapeziums have only a single pair of parallel sides. Kites have no parallel sides.
All quadrilateral angles must add up to 360 degrees. This is a key rule in geometry.
Quadrilaterals are all around us. Here are a few examples:
Quadrilaterals are simple, yet very important shapes in geometry. By learning about quadrilaterals, you can better understand the world of shapes. It will give you a strong foundation in geometry.
(Session 2025 - 26)