Rbse Solutions for Class 6 Chapter 4: Basic Geometrical Ideas

Rbse Solutions for Class 6 Chapter 4: Basic Geometrical Ideas

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Chapter 4 of RBSE Class 6 Maths, titled “Basic Geometrical Ideas,” introduces students to the fundamental concepts of geometry. This chapter covers the basics of points, lines, line segments, rays, angles, triangles, circles, and other geometric figures. Understanding these concepts will help students build a strong foundation in geometry and prepare for higher-level studies.

Below is a detailed solution for the RBSE Class 6 Maths Chapter 4: Basic Geometrical Ideas. These solutions are designed to assist students in understanding the key concepts and solving the exercises with ease.

Rbse Solutions for Class 6 Chapter 4: Basic Geometrical Ideas

NCERT Solutions for Class 6 Chapter 4: Basic Geometrical Ideas Exercise 4.1

1. Use the figure to name:

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 1

Solutions:

(a) The five points are D, E, O, B and C

(b) A line is
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 2

(c) Four rays are
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 3,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 4,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 5and
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 6.

(d) Five line segments are
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 7,
NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 8,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 9,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 10and
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 11

2. Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 12

Solutions:

The lines are
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 13,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 14,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 15,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 16,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 17,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 18,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 19,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 20,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 21,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 22,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 23,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 24

3. Use the figure to name:

(a) Line containing point E

(b) Line passing through A

(c) Line on which O lies

(d) Two pairs of intersecting lines

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 25

Solutions:

(a) Line containing point E is
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 26

(b) Line passing through A is
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 27

(c) Line on which O lies is
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 28

(d) Two pairs of intersecting lines are
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 29,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 30and
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 31,
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 32

4. How many lines can pass through (a) one given point? (b) two given points?

Solutions:

(a) Countless lines can pass through a given point.

(b) Only one line can pass through two given points.

5. Draw a rough figure and label it suitably in each of the following cases.

(a) Point P lies on  .

(b)  and  intersect at M.

(c) Line l contains E and F but not D.

(d)  and  meet at O.

Solutions:

(a)

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 38

(b)

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 39

(c)

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 40

(d)

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 41

6. Consider the following figure of line . Say whether the following statements are true or false in the context of the given figure.

(a) Q, M, O, N, P are points on the line .

(b) M, O, N are points on a line segment  .

(c) M and N are the endpoints of the line segment .

(d) O and N are the endpoints of the line segment .

(e) M is one of the endpoints of the line segment .

(f) M is the point on ray .

(g) Ray
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 49 is different from ray  .

(h) Ray  is the same as ray  .

(i) Ray  is not opposite to ray .

(j) O is not an initial point of 

(k) N is the initial point of  and .

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 58

Solutions:

(a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

NCERT Solutions for Class 6 Chapter 4: Basic Geometrical Ideas Exercise 4.2

1. Classify the following curves as (i) Open or (ii) Closed

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.2 - 1

Solutions:

(a) The given curve is an open curve

(b) The given curve is closed curve

(c) The given curve is open curve

(d) The given curve is closed curve

(e) The given curve is closed curve

2. Draw rough diagrams to illustrate the following:

(a) Open curve

(b) Closed curve

Solutions

(a) The below figure is the open curve

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.2 - 2

(b) The below figure is the closed curve

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.2 - 3

3. Draw any polygon and shade its interior.

Solutions:

The below figure is the polygon with interior shade

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.2 - 4

4. Consider the given figure and answer the questions:

(a) Is it a curve?

(b) Is it closed?

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.2 - 5

Solutions:

(a) Yes, it is a curve

(b) Yes, it is a closed curve

5. Illustrate, if possible, each one of the following with a rough diagram:

(a) A closed curve that is not a polygon.

(b) An open curve made up entirely of line segments.

(c) A polygon with two sides.

Solutions:

(a) The below figure is the closed figure but not a polygon

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.2 - 6

(b) The below figure is an open curve made up entirely of line segments

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.2 - 7

(c) No, its not possible, as the polygon having least number of sides is a triangle which has three sides.

NCERT Solutions for Class 6 Chapter 4: Basic Geometrical Ideas Exercise 4.3

1. Name the angles in the given figure.

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.3 - 1

Solutions:

The angles are ∠DAB, ∠ABC, ∠BCD and ∠CDA

2. In the given diagram, name the points(s)

(a) In the interior of ∠DOE

(b) In the exterior of ∠EOF

(c) On ∠EOF

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.3 - 2

Solutions:

(a) The point in the interior of ∠DOE is A

(b) The point in the exterior of ∠EOF is C, A and D

(c) The points on ∠EOF are E, B, O and F

3. Draw rough diagrams of two angles such that they have

(a) One point in common

(b) Two points in common

(c) Three points in common

(d) Four points in common

(e) One ray in common

Solutions:

(a) O is the common point between ∠COD and ∠AOB

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.3 - 3

(b) O and B are common points between ∠AOB and ∠BOC

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.3 - 4

(c) O, E and B are common points between ∠AOB and ∠BOC

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.3 - 5

(d) O, E, D and A are common points between ∠BOA and ∠COA

NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.3 - 6

(e) OC is the common ray between ∠BOC and ∠AOC

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.3 - 7

Key Concepts Covered in Chapter 4: Basic Geometrical Ideas

  • Points, Lines, and Line Segments: Learning about the basic building blocks of geometry.
  • Rays and Angles: Understanding how angles are formed by rays and how to classify different types of angles.
  • Triangles and Circles: Exploring the properties of triangles and circles, and defining terms such as radius, diameter, and vertices.
  • Geometrical Figures: Identifying common geometrical shapes like squares, rectangles, and circles.

FAQs (Frequently Asked Questions)

1. What is the difference between a line segment and a ray?
A line segment has two endpoints, whereas a ray has one endpoint and extends infinitely in one direction.

2. What are the properties of a circle?
A circle is a round shape with all points on its circumference equidistant from the center. It has a radius, diameter, and circumference.

3. How do you define an angle?
An angle is formed when two rays meet at a common endpoint, known as the vertex.

4. What is a triangle, and how is it classified?
A triangle is a three-sided polygon. Triangles can be classified based on their sides (equilateral, isosceles, or scalene) or based on their angles (acute, obtuse, or right).

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