Quadrilaterals

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

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