# 4th Class Mathematics Geometrical Figures Geometrical Figures

## Geometrical Figures

Category : 4th Class

Geometrical Figures

Introduction

In our day to day life we come across a number of objects. All the objects has a specific shape and size.

We recognize a number of objects by their shape. Therefore, to know about the objects and of their shapes is very important. In this chapter we will study about the shapes of different geometrical figures.

Point

To show a particular location, a dot (.) is placed over it, that dot is known as a point.

A is a point

Line Segment

Line segment is defined as the shortest distance between two fixed points. It has fixed length.

•            Example

How many line segments are there in the following figure?

Solution:

There are 6 line segments in the given figure.

Ray

It is defined as the extension of a line segment in one direction up to infinity.

•            Example

How many rays are there in the following figure?

Solution:

There are 12 rays.

Line

Line is defined as the extension of a line segment up to infinite in either direction.

•            Example

How many lines are there in the following figure?

Solution:

There are two lines.

Angle

Inclination between two rays having common end point is called angle.

$\angle ABC$ is a angle

A Right Angle

An angle whose measure is exactly $90{}^\circ$ is a right angle.

$\angle ABC$is a right angle

An Acute Angle

An angle whose measure is less than $90{}^\circ$ is an acute angle.

$\angle DEF$ is an acute angle.

An Obtuse Angle

An angle whose measure is greater than 90° but less than 180° is an obtuse angle.

$\angle LMN$ is an obtuse angle

•            Example

The following angle is a_____.

Solution:

It is an obtuse angle, because its measure is greater than 90°.

Polygon

A Simple closed figure formed of three or more line segments is called a polygon.

Line segments which form a polygon are called its sides. The point at which two adjacent sides of a polygon meet/ is called a vertex of polygon. In the given figure, triangle, quadrilateral/ pentagon and hexagon, all are examples of polygon.

Types of Polygons

Regular and Irregular Polygon

A regular polygon has all sides equal and all angles equal, otherwise, it is an irregular polygon.

Simple and Complex Polygon

A simple polygon has only one boundary and it does not cross over itself A complex polygon intersects itself.

Names of Polygons

Names of polygons based on their number of sides are given in the following table:

 Name Number of Sides Number of vertices Number of Angle Shape Triangle 3 3 3 Quadrilateral 4 4 4 Pentagon 5 5 5 Hexagon 6 6 6

Triangle

The geometrical shapes having three sides are called triangles. There are various types of triangles.

Equilateral Triangle

A triangle whose all sides are equal is called equilateral triangle.

Triangle ABC is an equilateral triangle.

Isosceles Triangle

A triangle whose two sides are equal is called isosceles triangle.

In triangle $ABC\text{ }AB=AC=4\text{ }cm$ hence, triangle ABC is an isosceles triangle,

Scalene Triangle

A triangle whose sides are unequal is called scalene triangle. In the figure below side lengths of triangle ABC are not equal hence, triangle ABC is a scalene triangle.

A Right Angle Triangle

A triangle whose one angle is a right angle is called right angled triangle. In the picture below triangle ABC is a right angle.

Acute Angled Triangle

A triangle with all the angles as acute angles is called acute angled triangle.

Obtuse Angled Triangle

A triangle with one angle as obtuse angle and other two angles are acute angles is called an obtuse angled triangle.

•            Example

Name the triangle whose all sides are equal.

Solution:

Equilateral triangle

•      Example

Name the triangle given below

Solution:

Right angled triangle because one angle is right angle.

The geometrical figure having four sides is called quadrilateral.

Rectangle

Rectangle is a quadrilateral in which:

(i)     All angles are of$90{}^\circ$.

(ii)    Opposite sides are equal.

Square

Square is a quadrilateral/ in which:

(i)     All angles are of $90{}^\circ$

(ii)    All sides are equal

Note: Sum of the angles of a quadrilateral is $360{}^\circ$ and sum of all the interior angles of a triangle is $180{}^\circ$

Circle

Circle is a closed curved line whose all points are at the same distance from a given point in a plane.

In the above circle, O is the centre of the circle. OA, OB and OC are radius of the circle. AB is the diametre of the circle.

Chord

A line segment joining two distinct points which lie on the circle is called chord of the circle.

In the figure given above DE and AB are chords of the circle.

Radius of a circle is half of the diametre.

In the figure given under circle, OA, OB and OC are radius of the circle.

Diametre

Diametre is the largest chord of the circle.

In the figure given under circle, AB is the diametre of the circle.

•            Example

Diametre of a circle is 8 cm. Find the radius of the circle.

Solution:

$Radius=\frac{Diametere}{2}=\frac{8}{2}\text{ }cm=4\text{ }cm$.

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