Every closed figure has a definite shape. The shape of an object depends on the number of sides and angles constituting it. Now, depending on the measurement of lengths of sides and degree of angles, varying shapes can be formed. One such shape is a quadrilateral. In the chapter below we shall learn about Quadrilaterals and Types of Quadrilaterals

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Quad means four and lateral means sides. All closed figures with four sides are called quadrilaterals. The sides of the quadrilateral may be equal, unequal, parallel or irregular which forms the basis of varying shapes in these four-sided shapes. Whatever may be the external shape, every quadrilateral has four sides, four vertices and with all its angles adding up to be 360 °.

The most common types of quadrilaterals are Squares and Rectangles. We have been studying about these basic quadrilaterals since our primary classes, but in this part of the chapter we shall bring in light various other types of the quadrilateral, which show properties like square or rectangle yet are not named so.

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The various types of quadrilaterals are

### 1. Parallelogram

As the name suggests, a parallelogram is a quadrilateral with parallel opposite sides. In a parallelogram all the opposite sides are equal and the angles made by each opposite side is also equal. In the figure shown below, PQRS is a quadrilateral and since PQ || RS and PS || QR we call it a parallelogram

### 2. Rectangle

The Rectangle is also a type of parallelogram with a little difference in the angles of the sides. In a rectangle, all the sides are at the right angle or to say perpendicular to each other. The figure below shows a quadrilateral ABCD and since all its sides are parallel to each other we may also call it a type of parallelogram with line segments placed at right angle to each other. This can be written as AB || CD and AC || BD. ∠A =∠B =∠C=∠D= 90°

### 3. Square

A square is a quadrilateral with all four sides equal. Every vertex of a square makes a right angle with its sides. A square is a quadrilateral which shows the following characteristic:

WX || YZ and WY || XZ. ∠W =∠X =∠Y=∠Z= 90°

### 4. Rhombus

A rhombus is also a parallelogram but with all sides equal. In other words, a parallelogram that shows e resemblance to a square as regards its lengths of sides is called a rhombus. These are sometimes referred to as Diamonds also. Rhombus shows a very peculiar feature regarding their diagonals. The diagonals in a rhombus meet exactly in the middle at a right angle and are said to bisect with each other.

In the figure above we see that STUV is a quadrilateral with sides ST || UV and SV || TU. All its sides are equal, thus ST=TU=UV=VS which also happen to form equal angles.

### 5. Trapezium

Amongst the other types of quadrilaterals, a trapezium shows different characteristics, In a trapezium, only one pair of the four sides are parallel to each other. In a trapezium,   all the sides may not be equal in measurement but one of the pairs of sides has to be parallel to each other.

In the above figure, we can see a trapezium with sides AB || DC. A trapezium does not show similarity in lengths and angles of sides hence is an irregular quadrilateral.

Every time we see a tabletop or a handkerchief what comes to our minds are the common type of quadrilaterals, a rectangle or a square. But from this chapter, we have come to know that every quadrilateral is not just a rectangle or square. So the next time you see a four-sided figure, just refer to it as a quadrilateral and reach to conclusions only when you compare it with the rest!

## Solved Example for You

Question 1: What is the similarity between a square and a rectangle

Answer : The line segments of both the closed figure shapes are placed at 90° to each other.

Question 2: Name the seven types of quadrilaterals?

Answer: A quadrilateral refers to a four-sided polygon that has four angles. The seven types of quadrilaterals are parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid.

Question 3: What is meant by a trapezoid?

Answer: A trapezoid refers to a 4-sided flat shape with straight sides and it has a pair of parallel opposite sides. It refers to a quadrilateral with exactly one pair of parallel sides. Furthermore, the parallel sides of a trapezium are known as bases.

Question 4: Explain the rectangle shape?

Answer: A rectangle refers to a quadrilateral that consists of four right angles. It is also an equiangular quadrilateral. Also, equiangular means that all of its angles happen to be equal (360°/4 = 90°). One can also define it as a parallelogram involving a right angle.

Question 5: Can we say that a diamond is a quadrilateral?

Answer: A quadrilateral refers to a polygon that consists of 4 sides and 4 corners.  A rhombus refers to a quadrilateral that has four sides of the same length. A diamond shape is certainly an example of a rhombus. Therefore, a diamond is a quadrilateral.

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