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Chapter 3 – Understanding Quadrilaterals

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Take a look around you. Can you see different structures with different sides and angles? When you eat bread, do you notice that it has 4 sides which are equal? Or when a kite flies in the sky you notice it has 4 sides but at different angles? Have you observed the structure of the beehive? Other objects around you like table, blackboard, television, bed and many more have more than three sides and varying angles. They consist of polygons. While understanding quadrilaterals you must be able to differentiate between them since there are many kinds of quadrilaterals based on their properties, such as a parallelogram, kite and trapezium. There are some special parallelograms as well which show similar and dissimilar properties with each other like rectangle, square and rhombus.

The above mentioned structures are called polygons but what is its meaning? Poly means many. Polygons are closed structures made up of only line segments. 

Classification of Polygons

Compare the carpet at your home and a beehive. Can you tell the difference between these two? Even though they are both polygons, a carpet has 4 sides while the beehive has 6 sides. This is how you can easily study polygons by classifying them on the basis of their vertices or number of sides. Polygon with three sides is called a triangle, those with four sides are called quadrilaterals, while those with five sides are called pentagons. Polygons having 6 sides like a beehive, are called hexagons, those with seven sides are heptagon and so on.

Quadrilaterals are the polygons which have 4 sides or vertices but different interior angles.

Look at your table and kite. Even though both of them have the same number of sides, the angles present inside them are different.

Quadrilaterals can be either concave or convex. What do you understand by these two terms? In convex quadrilateral, no portion of their diagonal is in the exterior while in concave they are in the exterior as well. Also, the sum of every interior angle in convex quadrilateral is less than 180°.

Sum of all the interior angles of a quadrilateral is 360° which is the angle sum property. Interior angle is formed as a result of intersection between two sides.

Later on, we shall discuss the term, diagonal. What does it mean? Diagonals connect two opposite vertices with each other.

Based on the nature of the sides and angles, quadrilaterals are further classified into different types.

Trapezium

Take a look at the tents. If you look from front you can see a structure of 4 sides out of which two are parallel. This is a trapezium. Quadrilaterals which have a pair of equal parallel sides are called trapezium. Non parallel sides are not equal to each other. A trapezium cannot be called a parallelogram.  

Kite

You can imagine the structure of a kite from the name itself. In a kite, two consecutive sides are equal to each other. It has 4 sides like A, B, C and D. AB=BC and CD=AD. Even though a kite is a quadrilateral but it is not a parallelogram.

Parallelogram

Parallelogram is a quadrilateral having two pairs of parallel sides. This pair is made up of opposite sides. They are equal in length as well. Opposite sides and angles of parallelogram are equal. Both the diagonals intersect at the centre. A parallelogram is a trapezium but trapezium is not a parallelogram.

Some special parallelograms

Rhombus

In a rhombus, all the sides are equal and parallel to each other but the interior angles are not right angles. It shows all the properties of a parallelogram. It is like a kite but tilted one. Diagonals of a rhombus are perpendicular bisectors of one another.

Rectangle

It is a quadrilateral in which parallel sides are equal in length. Each interior angle inside the rectangle measures 90° i.e. right angle. A rectangle is a parallelogram but not a square. Diagonals of the rectangle are equal in length. These diagonals bisect each other.

Square

In a square, all the sides are parallel to each other and equal in length. Each angle measures 90°. This means internal angles are right angles. It is a rectangle and rhombus as well. In a square, diagonals bisect each other at right angles and they are equal in length as well.

Q1. What do you mean by understanding Quadrilaterals?

A1. Understanding quadrilaterals means differentiating them on the basis of their properties, angles and sides.

Q2. How do you study Quadrilaterals?

A2. We can study quadrilaterals with the help of their interior angles, diagonals, angles, length and nature of sides.

Q3. What is a quadrilateral?

A3. In a trapezium if the sum of all the angles is equal to 360°, it is called a quadrilateral.

Q4. What is convex quadrilateral?

A4. Convex quadrilaterals are those with interior angles less than 180°.

Q5. What are 4 types of quadrilaterals?

A5. Four types of quadrilaterals are rhombus, square, rectangle, trapezium and kite.

By reading the above article, you must have understood the concept of quadrilateral, but to get a better insight download the MSVgo app.

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