Maths Class 9 Chapter 8 Quadrilaterals

# Maths Class 9 Chapter 8 Quadrilaterals

Important Concepts and Formulas

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

2.      Properties of a parallelogram:

i.                    A diagonal of a parallelogram divides it into two congruent triangles.
ii.                  The opposite sides of a parallelogram are equal.
iii.                The opposite angles of a parallelogram are equal.
iv.                The diagonals of a parallelogram bisect each other.

3.      A quadrilateral is a parallelogram, if its

i.                    opposite sides are equal, or
ii.                  opposite angles are equal, or
iii.                diagonals bisect each other, or
iv.                a pair of opposite sides is parallel and equal.

4.      The diagonals of a rectangle bisect each other and are equal.

5.      If the diagonals of a parallelogram are equal, then it is a rectangle.

6.      The diagonals of a rhombus bisect each other at right angles.

7.      If the diagonals of a parallelogram bisect each other at right angles, then it is a rhombus.

8.      The diagonals of a square bisect each other at right angles and are equal.

9.      If the diagonals of a parallelogram bisect each other at right angles and are equal, then it is a square.

10. The quadrilateral formed by joining the mid-point of the sides of a quadrilateral, in order, is a parallelogram.

11. Mid-point Theorem: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it.

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