1. Introduction to Quadrilaterals
– Definition of quadrilateral
– Properties of quadrilaterals
– Types of quadrilaterals
2. Types of Quadrilaterals
– Parallelogram
– Rectangle
– Square
– Rhombus
– Trapezium
– Kite
3. Properties of a Parallelogram
– Opposite sides are equal
– Opposite angles are equal
– Diagonals bisect each other
– Adjacent angles are supplementary
4. Special Parallelograms
– Rectangle: Properties and proof of diagonals being equal
– Rhombus: Properties and proof of diagonals bisecting at right angles
– Square: Properties as a combination of rectangle and rhombus
5. Conditions for a Quadrilateral to be a Parallelogram
– One pair of opposite sides is equal and parallel
– Both pairs of opposite angles are equal
– Diagonals bisect each other
– Both pairs of opposite sides are equal
6. Mid-Point Theorem
– Statement and proof
– Application to quadrilaterals
7. Theorems Related to Quadrilaterals
– Theorems proving properties of parallelograms
– Proofs of the conditions for a quadrilateral to be a parallelogram
8. Exercises and Practical Problems
– Solving problems based on the properties of quadrilaterals
– Application of mid-point theorem
– Verification of properties through examples
