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  • Maths Class 9

Notes Class 9 Maths Chapter 8 Quadrilaterals

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Notes For All Chapters Maths Class 9

1. Quadrilateral: A plane figure bounded by four lines segment AB, BC, CD and DA is called a quadrilateral.

Quadrilaterals Class 9 Notes Maths Chapter 9 1

The sum of the angles of a quadrilateral is 360°.

2. Various Types of Quadrilaterals

(i) Parallelogram: A quadrilateral in which opposite sides are parallel is called parallelogram and it is written as Parallelogram.
Quadrilaterals Class 9 Notes Maths Chapter 9 2

(ii) Rectangle: A parallelogram each of whose angle is 90°, is called a rectangle.
Quadrilaterals Class 9 Notes Maths Chapter 9 3

(iii) Square: A rectangle having all sides equal, is called a square.

Quadrilaterals Class 9 Notes Maths Chapter 9 4

(iv) Rhombus: A parallelogram having all sides equal is called a rhombus.
Quadrilaterals Class 9 Notes Maths Chapter 9 5

(v) Trapezium: A quadrilateral in which two opposite sides are parallel and two opposite sides are non-parallel is called a trapezium.
If two non-parallel sides of a trapezium are equal, then it is called an isosceles trapezium.
Quadrilaterals Class 9 Notes Maths Chapter 9 6

(vi) Kite: A quadrilateral in which two pairs of adjacent are equal is known as the kite.
Quadrilaterals Class 9 Notes Maths Chapter 9 7

3. Important Theorems

  • The sum of all the four angles of a quadrilateral is 360°.
  • A diagonal of a parallelogram divides it into two congruent triangles.
  • A quadrilateral is a parallelogram if
    • opposite sides are equal.
    • opposite angles are equal,
    • diagonals bisect each other.
  • A quadrilateral is a parallelogram if
    • its opposite angles are equal.
    • its opposite sides are equal.
    • its diagonals bisect each other.
    • a pair of opposite sides is equal and parallel.
  • Diagonals of a rectangle bisect each other and they are equal and vice-versa.
  • Diagonals of a rhombus bisect each other at right angles and they are not equal and vice-versa.
  • Diagonals of a square bisect each other at right angles and they are equal and vice-versa.
  • The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it. (Mid-point theorem)
  • The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point. (By converse of mid-point theorem)
  • The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, taken in order, is a parallelogram.
  • In a quadrilateral, if diagonals bisect each other, then it forms a parallelogram.

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