NCERT Solutions for Class 6 Maths, Chapter 4 - Basic Geometrical Ideas

The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing etc. You observe and use different objects like boxes, tables, books, the tiffin box you carry to your school for lunch, the ball with which you play and so on. All such objects have different shapes. The ruler which you use, the pencil with which you write are straight. The pictures of a bangle, the one rupee coin or a ball appear round. In this chapter, you will learn some interesting facts that will help you know more about the shapes around you.

In NCERT Maths Book Class 6, Chapter 4 Solutions, as you progress through the chapter you will learn some basic geometrical ideas. The point, line, distinct lines, line segments are some of the important and basic topics of geometry. As you move further in this chapter you will learn more about line segments, rays, curve and polygons. An angle is made up of two rays starting from a common point. Towards the end of this chapter, you will study some shapes like triangles, quadrilaterals and circles. Further, you will learn the parts of a circle namely chord, diameter, sector and segment.

Let’s take a look at topics and sub-topics of Class 6 Maths Chapter 4, Basic Geometrical Ideas

4.1 Introduction

4.2 Points

4.3 A Line Segment

4.4 A-Line

4.5 Intersecting Lines

4.6 Parallel Lines

4.7 Ray

4.8 Curves

4.9 Polygons

4.10 Angles

4.11 Triangles

4.12 Quadrilaterals

4.13 Circles

In Class 6 Maths NCERT Solutions Chapter 4, you will learn – 

Section 4.2 – In this section, you will study points. The almost invisible tiny dot will give you the idea of a point. A point determines a location. It is usually denoted by a capital letter. For example, points marked by the letters A, B and C are read as point A, point B and point C.

Section 4.3 –  You have studied points in the previous section. Now you will learn the line segment. Fold a piece of paper and unfold it. You will see a fold. This will give you the idea of a line segment. Take a thin thread and hold its two ends and stretch it without a slack. It represents a line segment. A line segment corresponds to the shortest distance between two points. The line segments joining point A and B is denoted by AB and BA denotes the same line segment.

Section 4.4 – This section will brief you about a line. A line is obtained when a line segment like AB is extended on both sides indefinitely. It is denoted by AB or sometimes by a single small letter like l. It contains a countless number of points. Two points are enough to fix a line. We say ‘two points determine a line’.

Section 4.5 – Now you will learn interesting lines. Two distinct lines meeting at a point are called intersecting lines. Interesting lines have one common point.

Section 4.6 –  In this section, you will study parallel lines. Two lines in a plane are said to be parallel if they never meet. We can think of parallel lines with the help of some examples like a ruler, in which the opposite edges never meet, the crossbars of a window, rail lines etc.

Section 4.7 – You already what a line is. Now you will study a portion of a line which is termed as a ray. A ray starts from a point and goes in one direction endlessly. We can think of rays with the help of some examples like the beam of light from a lighthouse, a ray of light from a torch and sun rays.

Section 4.8 – This section will brief you about curves. A simple curve is one that does not cross itself. As you move further in this section you will study the categories in curves. A curve is said to be closed if it ends are joined otherwise it is said to be open.

Section 4.9 – This section will give you an introduction to shapes with the help of polygons. A polygon is a simple closed curve made up of line segments. Here the line segments are the sides of the polygon. Any two sides with a common endpoint are adjacent sides. The meeting point of a pair of sides is called a vertex. The endpoints of the same side are adjacent vertices. The join of any two non-adjacent vertices is diagonal.

Section 4.10 –  In this section, you will study angles. An angle is made up of two rays starting from a common endpoint. Two rays OA and OB make angle AOB or also called angle BOA. An angle leads to three divisions of a region: On the angle, the interior of the angle and the exterior of the angle.

Section 4.11 –  You have studied what a polygon is. Now you will study some categories of polygons. A triangle is a three-sided polygon. A triangle can be made up of three line segments, or three rays or three lines. Being a polygon, a triangle has an exterior and an interior.

Section 4.12 –  This section will teach you another category of polygons. A quadrilateral is a four-sided polygon. It should be named cyclically. In any quadrilateral ABCD, AB & DC and AD & BC are pairs of opposite sides. Angle A & angle C and angle B & angle D are pairs of opposite angles. Further, angle A is adjacent to angle B and angle D. Similar relations exist for the other three angles.

Section 4.13 – Towards the end of this chapter, you will study circles. In our environment, you find things that are round, a wheel, a bangle, a coin etc. We use the round shape in many ways. It is easier to roll a steel tube than to drag it. A circle is a simple closed curve which is not a polygon. It is the path of a point moving in the same direction from a fixed point. The fixed point is the centre, the fixed distance is the radius, and the distance around the circle is the circumference. As you move further in this section you will learn the parts of a circle. A chord of a circle is a line segment joining any two points on the circle. A diameter is a chord passing through the centre of the circle. A sector is a region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides. A segment of a circle is a region in the interior of the circle enclosed by an arc and a chord.

In this chapter, you are provided with several examples along with their solutions for a clear understanding of basic ideas of geometry. To know more about NCERT Solutions for Class 6 Maths Chapter 4 Basic Ideas Of Geometry., you should explore the exercises below. You can also download the Basic Ideas Of Geometry Class 6 NCERT Solutions PDF, solved by expert maths trainers. You can also refer online to Class 6 Maths Chapter 4 Worksheet PDF.