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Mathematics Class 9 - Quadrilaterals Notes

Comprehensive study notes for Class 9 - Quadrilaterals olympiad preparation

Quadrilaterals

In this chapter, you will learn about quadrilaterals, their types, properties, and how to identify and classify them. By the end of this chapter, you will be able to recognize different quadrilaterals and solve problems related to their angles and sides.

Key Concepts

  • Quadrilateral: A polygon with four sides and four angles.
  • Vertices: The corners of a quadrilateral.
  • Diagonals: Line segments joining opposite vertices.

Types of Quadrilaterals

  • Parallelogram: Opposite sides are parallel and equal.
  • Rectangle: All angles are right angles; opposite sides are equal and parallel.
  • Square: All sides are equal; all angles are right angles.
  • Rhombus: All sides are equal; opposite angles are equal.
  • Trapezium: Only one pair of opposite sides is parallel.
  • Kite: Two pairs of adjacent sides are equal.

Properties of Quadrilaterals

  • The sum of the interior angles of a quadrilateral is always 360°.
  • Diagonals may or may not be equal, depending on the type.
  • Some quadrilaterals have lines of symmetry.

Special Quadrilaterals

  • Rectangle: Diagonals are equal and bisect each other.
  • Square: Diagonals are equal, bisect each other at right angles.
  • Rhombus: Diagonals bisect each other at right angles but are not equal.
  • Parallelogram: Opposite sides and angles are equal; diagonals bisect each other.

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 right angles?
  4. How many diagonals does a quadrilateral have?
  5. State two properties of a parallelogram.

Challenge Yourself

  • Draw a quadrilateral and label its sides, angles, and diagonals.
  • Classify the following as parallelogram, rectangle, square, rhombus, trapezium, or kite:
    a) A shape with all sides equal and all angles right angles.
    b) A shape with only one pair of parallel sides.
    c) A shape with opposite sides equal and all angles right angles.

Did You Know?

  • A square is a special type of rectangle and rhombus.
  • The diagonals of a kite are perpendicular to each other.

Glossary

  • Quadrilateral: A four-sided polygon.
  • Diagonal: A line joining two opposite vertices.
  • Parallel: Lines or sides that are always the same distance apart.
  • Symmetry: When one half of a shape is a mirror image of the other half.

Answers to Practice Questions

  1. 360°
  2. Trapezium
  3. Square
  4. Two
  5. Opposite sides are parallel and equal; diagonals bisect each other.

Explore different quadrilaterals and their properties to master geometry!

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