1. Overview of Quadrilateral Types
A quadrilateral is a four-sided closed figure. Depending on side lengths, angles, and diagonal properties, quadrilaterals are grouped into several special types such as parallelogram, rectangle, square, rhombus, trapezium, and kite.
This topic helps you recognise each type based on its key features so you can identify them instantly in diagrams and solve questions faster.
2. Classification Based on Sides and Angles
One way to classify quadrilaterals is by observing which sides or angles are equal. These are often the first clues in diagram-based questions.
2.1. Equal Sides
Quadrilaterals like rhombus and square have all four sides equal. Parallelograms have equal opposite sides.
2.2. Right Angles
Rectangles and squares have all interior angles equal to \(90^\circ\), making them right-angled quadrilaterals.
2.3. Parallel Sides
Parallelograms, rectangles, and squares have two pairs of parallel sides, while trapeziums have at least one pair of parallel sides.
3. Classification Based on Diagonals
Diagonals help identify special quadrilaterals because each type has unique diagonal properties such as equality, perpendicularity, or bisection.
3.1. Equal Diagonals
Rectangles and squares have diagonals of equal length.
3.2. Perpendicular Diagonals
In kites and rhombuses, the diagonals intersect at right angles.
3.3. Diagonals that Bisect Each Other
Parallelograms, rectangles, squares, and rhombuses have diagonals that cut each other into two equal halves.
4. Hierarchy of Quadrilaterals
Quadrilaterals form a family tree where some shapes are special cases of others. Understanding this hierarchy helps you remember their relationships.
4.1. Parallelogram Family
A parallelogram is the parent shape for several special quadrilaterals. Each special case has additional properties.
4.1.1. Rectangle
A parallelogram with all angles equal to \(90^\circ\).
4.1.2. Rhombus
A parallelogram with all four sides equal.
4.1.3. Square
A parallelogram with all sides equal and all angles \(90^\circ\). It is both a rectangle and a rhombus.
4.2. Other Quadrilaterals
Kites and trapeziums do not belong to the parallelogram family. They form their own separate groups based on side and diagonal properties.