CBSE Class 9 Mathematics Quadrilaterals Notes Set 02

A quadrilateral is a closed figure obtained by joining four point (with no three points collinear) in an order.
Every quadrilateral has : (i) Four vertices, (ii) Four sides, (iii) Four angles and (iv) Two diagonals.

SUM OF THE ANGLES OF A QUADRILATERAL
Statement: The sum of the angles ofa quadrilateral is 360°

TYPES OF QUADRILATERALS
1. Trapezium : It is quadrilateral in which one pair of opposite sides are parallel.
2. Parallelogram : It is a quadrilateral in which both the pairs of opposite sides are parallel.
3. Rectangle : It is a quadrilateral whose each angle is 90°. ABCD is a rectangle.
(i) ∠A+ ∠B = 90° + 90° = 180° ⇔ AD || BC
(ii) ∠B+ ∠C= 900 + 900 = 180° ⇔ AB || DC

Rectangle ABCD is a parallelogram also.
4. Rhombus : It is a quadrilateral whose all the sides are equal.
5. Square : It is a quadrilateral whose all the sides are equal and each angle is 90°.
6. Kite : It is a quadrilateral in which two pairs of adjacent sides are equal.
Note :
• Square, rectangle and rhombus are all parallelograms.
• Kite and trapezium are not parallelograms.
• A square is a rectangle.
• A square is a rhombus.
• A parallelogram is a trapezium.

PARALLELOGRAM:
A parallelogram is a quadrilateral in which opposite sides are parallel. It is denoted by

PROPERTIES OF PARALLELOGRAM:
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. The opposite sides of a parallelogram are equal.
Theorem : If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
3. The opposite angles of a parallelogram are equal.
Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
4. The diagonals of a parallelogram bisect each other.
Theorem : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

MID POINT THEOREM
(BASIC PROPORTIONALITY THEOREM)

Statement 1:
The line segment joining the mid-points of any two sides of a triangle is parallel to the third side

Statement 2:
The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.