Class 9 | Mathematics
Topic Tree
- Properties of a parallelogram
- Theorems 1 to 7
- The mid-point theorem
- Theorems 8 and 9
Terms, Definitions and Symbols
1. Definition of a Quadrilateral:
– A quadrilateral is a polygon with four sides.
2. Types of Quadrilaterals:
– Parallelogram
– Rectangle
– Square
– Rhombus
– Trapezium
– Kite
3. Properties of a Parallelogram:
– Opposite sides are parallel.
– Opposite angles are equal.
– Consecutive angles are supplementary.
4. Properties of a Rectangle:
– All angles are right angles (90 degrees).
– Opposite sides are equal in length.
– Diagonals are equal in length and bisect each other.
5. Properties of a Square:
– All angles are right angles (90 degrees).
– All sides are equal in length.
– Diagonals are equal in length and bisect each other at right angles.
6. Properties of a Rhombus:
– Opposite sides are parallel.
– All sides are equal in length.
– Diagonals are perpendicular and bisect each other.
7. Properties of a Trapezium:
– At least one pair of opposite sides is parallel.
8. Properties of a Kite:
– Two pairs of adjacent sides are equal in length.
– Diagonals intersect at right angles.
9. Sum of Interior Angles in a Quadrilateral:
– The sum of the interior angles of any quadrilateral is always 360 degrees.
10. Exterior Angles of a Quadrilateral:
– The sum of the four exterior angles of a quadrilateral is always 360 degrees.
Angle 1 + angle 2 + angle 3 + angle 4 = 360 degree
11. Mid-Point Theorem:
– In a quadrilateral, the line segment joining the mid-points of two sides is parallel to the third side and half of its length.
12. Diagonals of a Quadrilateral:
– In a parallelogram, the diagonals bisect each other.
– In a rectangle, square, or rhombus, the diagonals are equal and bisect each other at right angles.
– In a kite, the diagonals are perpendicular, and one of the diagonals bisects the other.
