Quadrilateral property for basic maths class 7-10

Quadrilateral

1. Quadrilaterals - Class 9 Mathematics Understanding Properties, Types, and Theorems

2. What is a Quadrilateral? A quadrilateral is a closed polygon with four sides, four vertices, and four angles. The sum of its interior angles is always 360°.

3. Types of Quadrilaterals 1. Parallelogram 2. Rectangle 3. Square 4. Rhombus 5. Trapezium 6. Kite

4. Properties of a Parallelogram 1. Opposite sides are equal and parallel. 2. Opposite angles are equal. 3. Diagonals bisect each other. 4. Sum of adjacent angles is 180°.

5. Properties of a Rectangle 1. Opposite sides are equal and parallel. 2. All angles are 90°. 3. Diagonals are equal and bisect each other.

6. Properties of a Square 1. All sides are equal. 2. All angles are 90°. 3. Diagonals are equal, bisect each other at 90°, and bisect the angles.

7. Properties of a Rhombus 1. All sides are equal. 2. Opposite angles are equal. 3. Diagonals bisect each other at 90°. 4. Diagonals bisect the angles.

8. Properties of a Trapezium 1. One pair of opposite sides is parallel. 2. Adjacent angles on the same side of a non-parallel side are supplementary.

9. Midpoint Theorem The line joining the midpoints of two sides of a triangle is parallel to the third side and is half of its length.

10. Theorem on Diagonals of a Parallelogram In a parallelogram, the diagonals bisect each other.

11. Example Problem In a parallelogram ABCD, diagonal AC = 10 cm and diagonal BD = 8 cm. Find the length of AO and BO. Solution: Since diagonals bisect each other, AO = 5 cm, BO = 4 cm.

12. Conclusion • Quadrilaterals have unique properties based on their types. • Understanding theorems helps solve complex problems. • Practice with real-life examples for better understanding.