### Theory:

A four-sided closed two-dimensional shape is called a quadrilateral.
Types of quadrilateral
 Name Picture Properties Parallelogram 1. Opposite sides are equal and parallel. 2. Opposite angles are equal. 3. Diagonals bisect each other. Square 1. All sides are equal and parallel. 2. All interior angles are $$90^\circ$$. 3. Diagonals bisect each other at right angles. Rectangle 1. Opposite sides are equal and parallel. 2. All interior angles are $$90^\circ$$. 3. Diagonals bisect each other. Rhombus 1. All sides are equal. 2. Opposite angles are equal. 3. Diagonals are perpendicular. Trapezium 1. The bases of a trapezium are parallel. 2. Sum of adjacent angles on non-parallel sides are supplementary. Kite 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.