CBSE Class 9 Mathematics Quadrilaterals Notes

 Chapter 8

Quadrilaterals

Chapter Notes

Top Definitions

1. A quadrilateral is a closed figure obtained by joining four points (with no three points collinear) in an order.

2. A diagonal is a line segment obtained on joining the opposite vertices.

3. Two sides of a quadrilateral having no common end point are called its opposite sides.

4. Two angles of a quadrilateral having common arm are called its adjacent angles.

5. Two angles of a quadrilateral not having a common arm are called its opposite angles.

6. A trapezium is quadrilateral in which one pair of opposite sides are parallel.

7. In the non – parallel sides of trapezium are equal, it is known as isosceles trapezium.

8. A parallelogram is a quadrilateral in which both the pairs of opposite sides are parallel.

9. A rectangle is a quadrilateral whose each angle is 90°

10. A rhombus is quadrilateral whose all the sides are equal.

11. A square is a quadrilateral whose all sides are equal and each angle is 90°.

12. A kite is a quadrilateral in which two pairs of adjacent sides are equal.

Top Concepts

1. Properties of parallelogram:

i) The opposite sides of a parallelogram are parallel.

ii) A diagonal of a parallelogram divides it in two congruent triangles.

iii) The opposite sides of a parallelogram are equal.

iv) The opposite angles of a parallelogram are equal.

v) The consecutive angles (conjoined angles) of a parallelogram are supplementary.

vi) The diagonals of a parallelogram bisect each other.

2. A diagonal of a parallelogram divides the parallelogram into two congruent triangles.

3. In a parallelogram opposite sides are equal.

4. If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

5. In a parallelogram opposite angles are equal.

6. If in quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

7. The diagonals of a parallelogram bisect each other.

8. If the diagonals of a quadrilateral bisect other, then it is a parallelogram.

9. A quadrilateral is a parallelogram, if a pair of opposite sides is equal and parallel.

10. Square, rectangle and rhombus are all parallelograms.

11. Kite and trapezium are not parallelogram.

12. A square is a rectangle.

13. A square is a rhombus.

14. A parallelogram is a trapezium.

15. Every rectangle is a parallelogram; therefore, it has all the properties of a parallelogram. Additional properties of a rectangle are:

i) All the (interior) angles of are rectangle are right angles.

ii) The diagonals of a rectangle are equal.

16. Every rhombus is a parallelogram; therefore, it has all the properties of a parallelogram. Additional properties of a rhombus are:

i) All the sides of rhombus are equal.

ii) The diagonals of a rhombus intersect at right angles.

iii) The diagonals bisect the angles of a rhombus.

17. Every square is a parallelogram; therefore, it has all the properties of a parallelogram. Additional properties of a rhombus are:

i) All the sides are equal

ii) All the angles are equal to 90° each

iii) Diagonals are equal 

iv) Diagonal bisect each other at right angle

v) Diagonals bisects the angles of vertex

18. Sum of all the angles of a quadrilateral is 3600.

19. Mid Point Theorem (Basic Proportionality Theorem): The line segment joining the mid point of any two sides of a triangle is parallel to the third sides and equal to half of it.

20. Converse of mid-point theorem: The line drawn through the mid-point of one side of a triangle parallel to the another side, bisects the third side.

21. If there are three or more parallel lines and the interests made by them on a transversal are equal, then the corresponding intercepts on any other transversal are also equal.

22. A quadrilateral formed by joining the mid-points of the sides of a quadrilateral, in order is a parallelogram.

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