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
Properties of Special Quadrilaterals:
Square:
- All sides are the same length.
- 2 pairs of parallel sides.
- All angles are 90°.
- Diagonals that bisect each other at 90°.
- 4 lines of symmetry.
- Order 4 rotational symmetry.
Rectangle:
- 2 pairs of sides of equal length.
- 2 pairs of parallel sides.
- All angles are 90°.
- Diagonals that bisect each other.
- 2 lines of symmetry.
- Order 2 rotational symmetry.
Rhombus:
- All sides are the same length.
- 2 pairs of parallel sides.
- Opposite angles are equal.
- Diagonals that bisect each other at 90°.
- 2 lines of symmetry.
- Order 2 rotational symmetry.
Parallelogram:
- 2 pairs of sides of equal length.
- 2 pairs of parallel sides.
- Opposite angles are equal.
- Diagonals that bisect each other.
- No lines of symmetry.
- Order 2 rotational symmetry.
Kite:
- 2 pairs of equal sides.
- No parallel sides.
- 1 pair of equal angles.
- 1 diagonal that bisects the other.
- Diagonals that cross at 90°.
- 1 line of symmetry.
- Order 1 rotational symmetry.
Trapezium:
- Sides of different lengths.
- 1 pair of parallel sides.
- Angles of different sizes.
- No lines of symmetry.
- Order 1 rotational symmetry.
Isosceles Trapezium:
- 2 sides the same length.
- 1 pair of parallel sides.
- 2 pairs of equal angles.
- 1 line of symmetry.
- Order 1 rotational symmetry.
