Class 8 Notes - Understanding Quadrilaterals

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Understanding Quadrilaterals

A quadrilateral is a polygon with four sides, four vertices, and four angles. In this chapter, you will learn about different types of quadrilaterals, their properties, and how to classify them.

1. What is a Quadrilateral?

  • A closed figure with four sides and four angles.
  • The sum of the interior angles of a quadrilateral is always 360°.
  • Examples: squares, rectangles, parallelograms, rhombuses, trapeziums, and kites.

2. 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 is equal.

3. Properties of Quadrilaterals

  • Four sides, four vertices, and four angles.
  • Sum of all interior angles is 360°.
  • Diagonals: A quadrilateral has two diagonals (lines joining opposite vertices).

4. Angle Sum Property

The sum of the four angles of any quadrilateral is always 360°.
Proof: Draw a diagonal to divide the quadrilateral into two triangles. Each triangle has an angle sum of 180°, so total = 180° + 180° = 360°.

5. Special Quadrilaterals

  • Parallelogram: Opposite sides and angles are equal, diagonals bisect each other.
  • Rectangle: All angles are right angles, diagonals are equal and bisect each other.
  • Square: All sides and angles are equal, diagonals are equal and bisect at right angles.
  • Rhombus: All sides are equal, diagonals bisect at right angles but are not equal.
  • Trapezium: Only one pair of sides is parallel.
  • Kite: Two pairs of adjacent sides are equal, diagonals are perpendicular.

6. Examples

  • A rectangle is a parallelogram with all angles 90°.
  • A square is a rectangle with all sides equal.
  • A rhombus is a parallelogram with all sides equal.

7. Practice Questions

  1. What is the sum of the interior angles of a quadrilateral?
  2. Name a quadrilateral with only one pair of parallel sides.
  3. Which quadrilateral has all sides equal and all angles 90°?
  4. Draw a kite and mark its equal sides and equal angles.
  5. If one angle of a quadrilateral is 90°, what can you say about the sum of the other three angles?

8. Real-Life Applications

  • Windows and doors (rectangles and squares)
  • Diamond-shaped road signs (rhombus)
  • Trapezium-shaped tables
  • Kite flying

9. Summary

  • A quadrilateral has four sides, four angles, and four vertices.
  • The sum of its interior angles is always 360°.
  • There are many types of quadrilaterals, each with special properties.