Class 9 Notes - Quadrilaterals

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Quadrilaterals

A quadrilateral is a polygon with four sides, four vertices, and four angles. The sum of the interior angles of a quadrilateral is always 360°.

Types of Quadrilaterals

  • Parallelogram: Opposite sides are parallel and equal, opposite angles are equal.
  • Rectangle: All angles are 90°, opposite sides are equal and parallel.
  • Square: All sides are equal, all angles are 90°, opposite sides are parallel.
  • Rhombus: All sides are equal, opposite angles are equal, diagonals bisect at right angles.
  • Trapezium (Trapezoid): Only one pair of opposite sides is parallel.
  • Kite: Two pairs of adjacent sides are equal, one pair of opposite angles are equal.

Properties of Quadrilaterals

  • Four sides, four vertices, and four angles.
  • The sum of the interior angles is 360°.
  • Diagonals may or may not be equal, depending on the type.
  • Some quadrilaterals have lines of symmetry (e.g., square, rectangle, rhombus).

Diagonals

  • A quadrilateral has two diagonals (lines joining opposite vertices).
  • In a rectangle and square, diagonals are equal and bisect each other.
  • In a rhombus, diagonals bisect each other at right angles but are not equal.

Examples in Daily Life

  • Chessboard squares (square)
  • Book cover (rectangle)
  • Diamond-shaped sign (rhombus)
  • Trapezium-shaped table
  • Kite (kite)

Important Formulas

  • Sum of interior angles = 360°
  • Area of rectangle = length × breadth
  • Area of square = side × side
  • Area of parallelogram = base × height
  • Area of rhombus = (1/2) × d1 × d2 (where d1 and d2 are diagonals)
  • Area of trapezium = (1/2) × (sum of parallel sides) × height

Sample Questions

  1. What is the sum of the interior angles of a quadrilateral?
  2. Which quadrilateral has all sides equal and all angles 90°?
  3. Give an example of a quadrilateral with only one pair of parallel sides.
  4. How many diagonals does a quadrilateral have?
  5. Find the area of a rectangle with length 8 cm and breadth 5 cm.

Practice Exercise

  • Draw and label different types of quadrilaterals in your notebook.
  • Measure the sides and angles of a rectangle and a square using a ruler and protractor.
  • Find objects at home that are shaped like a parallelogram or trapezium.

Summary

  • Quadrilaterals are four-sided polygons with a total angle sum of 360°.
  • There are various types of quadrilaterals, each with unique properties.
  • Understanding quadrilaterals helps in geometry, design, and real-life applications.