Type Of Quadrilaterals Notes For Class 9 Formulas Download PDF

Chapter 8 Classification of Quadrilaterals

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

(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.

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- Chapter 1 NUMBER SYSTEMS
- Chapter 2 POLYNOMIALS
- Chapter 3 COORDINATE GEOMETRY
- Chapter 5 INTRODUCTION TO EUCLID’S GEOMETRY
- Chapter 6 LINES AND ANGLES
- Chapter 7 TRIANGLES
- Chapter 12 HERON’S FORMULA
- Chapter 4 Equations In Two Variables
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 13 Volume and Surface Area
- chapter 14 Statistics
- Chapter 15 Probability
- Chapter 11: Constructions

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