Class 9 Mathematics: Quadrilaterals

• Introduction & Basics
  • Definition: A closed figure bounded by four line segments.
  • Angle Sum Property: Sum of all interior angles of a quadrilateral is $360^\circ$.
  • Types of Quadrilaterals
    • Trapezium: One pair of opposite sides is parallel.
    • Parallelogram: Both pairs of opposite sides are parallel.
    • Kite: Two pairs of adjacent sides are equal.
• Types of Parallelograms (Special Quadrilaterals)
  • Rectangle: Parallelogram with each angle equal to $90^\circ$.
  • Rhombus: Parallelogram with all sides of equal length.
  • Square: Parallelogram with equal sides and each angle equal to $90^\circ$.
• Properties of a Parallelogram
  • Diagonal property: Divides the parallelogram into two congruent triangles.
  • Side property: Opposite sides are equal.
  • Angle property: Opposite angles are equal.
  • Consecutive angles: Adjacent angles are supplementary (sum to $180^\circ$).
  • Diagonal bisector: Diagonals bisect each other.
• Conditions for a Quadrilateral to be a Parallelogram
  • Opposite sides are equal.
  • Opposite angles are equal.
  • Diagonals bisect each other.
  • One pair of opposite sides is equal and parallel.
• The Mid-Point Theorem
  • Theorem Statement: The line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it.
  • Converse Theorem: The line drawn through the mid-point of one side of a triangle, parallel to another side, bisects the third side.
  • Intercept Theorem: Line segments made on a transversal by three or more parallel lines.