Theory:

A four-sided closed two-dimensional shape is called a quadrilateral.
Types of quadrilateral
Name
Picture
Properties
Parallelogram
Parallelogram.png
1. Opposite sides are equal and parallel.
 
2. Opposite angles are equal.
 
3. Diagonals bisect each other.
Square
Square.png
1. All sides are equal and parallel.
 
2. All interior angles are \(90^\circ\).
 
3. Diagonals bisect each other at right angles.
Rectangle
Rectangle.png
 
1. Opposite sides are equal and parallel.
 
2. All interior angles are \(90^\circ\).
 
3. Diagonals bisect each other.
Rhombus
 Rhombus.png
1. All sides are equal.
 
2. Opposite angles are equal.
 
3. Diagonals are perpendicular.
Trapezium
 Trapezium.png
1. The bases of a trapezium are parallel.
 
2. Sum of adjacent angles on non-parallel sides are supplementary.
Kite
 Kite.png
1. Diagonals are perpendicular.
 
2. Diagonals bisect the vertex angles.
 
3. Non-vertex angles are congruent.
 
4. Two disjoint pairs of consecutive sides are congruent.
Properties of a quadrilateral
  • A quadrilateral can be regular or irregular.
  • A quadrilateral has \(4\) sides, \(4\) angles and \(4\) vertices.
  • The sum of all the interior angles of a quadrilateral is \(360^\circ\).
Constructing quadrilateral
We can construct a unique quadrilateral in five ways.

1. When four sides and one diagonal are given.

2. When two diagonals and three sides are given.

3. When two adjacent sides and three angles are given.

4. When three sides and two included angles are given.

5. When other special properties are known.