**Different Types of Quadrilaterals**

Quadrilaterals are categorised as the following, depending upon their sides.

- Parallelogram
- Rhombus
- Rectangle
- Square
- Trapezium
- Isosceles Trapezium
- Kite

- More Solved examples on Quadrilaterals
- Properties of Cyclic Quadrilaterals
- RS Aggarwal Class 9 Solutions Quadrilaterals and Parallelograms

**Parallelogram:** A quadrilateral in which the pairs of opposite sides are parallel, is called a parallelogram.

In a parallelogram,

- Opposite sides are equal and parallel, i.e., AB = DC, BC = AD, AB || DC, and BC || AD.
- Opposite angles are equal, i.e., ∠A = ∠C and ∠B = ∠D.
- Diagonals bisect each other, i.e., AO = OC and BO = OD.
- Diagonal divides the parallelogram into two congruent triangles, i.e., ΔADC and ΔABC are congruent and ΔADB and ΔCBD are congruent.

**Rectangle:** A parallelogram in which each angle is a right angle, is called a rectangle.

In a rectangle,

- Opposite sides are equal and parallel, i. e., AB = CD, AB || CD, BC = DA, and BC || DA.
- All angles are right angles, i.e., ∠A = ∠B = ∠C = ∠D = 90°.
- Both the diagonals are equal, i.e., AC = BD.
- Diagonals bisect each other, i.e., AR = RC and BR = RD.

**Rhombus:** A parallelogram in which all four sides are equal, is called a rhombus.

In a rhombus,

- All sides are equal, i.e., PQ = QR = RS = SR
- Opposite sides are parallel, i.e., PQ || SR and SP || RQ.
- Opposite angles are equal, i.e., ∠P = ∠R and ∠Q = ∠S
- Diagonals bisect each other at right angle, i.e., PO = OR, SO = OQ and ∠SOR = ∠SOP = ∠ROQ = ∠QOP = 90°.

**Square:** A rhombus with all its angles equal to right angle, is called a square.

In other words, a square is a rectangle in which all the four sides are equal.

In a square,

- Opposite sides are parallel, i.e., AB || DC and AD || BC.
- All the sides are equal, i.e., AB = BC = CD = DA.
- All the angles are equal to 90°, i.e., ∠A = ∠B = ∠C = ∠D = 90°
- The diagonals bisect each other at right angle,

i. e., AO = OC and BO = OD and ∠AOB = ∠BOC = ∠COD = ∠DOA = 90° - Both the diagonals are equal in length, i.e., AC = BD.

**Trapezium:** A quadrilateral in which one pair of opposite sides are parallel, is called a trapezium.

In a trapezium,

- A pair of opposite sides is parallel.
- Both the diagonals AC and BD are of different lengths.
- Diagonals do not bisect each other at right angle.
- Opposite angles are not equal.

**Isosceles trapezium:** A quadrilateral in which a pair of opposite sides is parallel and the other two sides are equal, is called an isosceles trapezium.

In an isosceles trapezium,

- A pair of opposite sides is parallel, i.e., AB || CD.
- Non-parallel sides are equal, i.e., AD = BC.
- Both the diagonals are equal, i.e., AC = BD.
- ∠A = ∠B and ∠D = ∠C.

**Kite:** A quadrilateral in which two pairs of adjacent sides are equal is called a kite.

In a kite,

- Two pairs of adjacent sides are equal, i.e., AB = AD and BC = CD.
- Diagonals intersect each other at right angle, i.e., ∠AEB = ∠AED = ∠BEC = ∠DEC = 90°.

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