**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.

### 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**

**Solutions:**

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

(b) A line is

(c) Four rays are

,

,

and

.

(d) Five line segments are

,

,

,

and

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

**Solutions:**

The lines are

,

,

,

,

,

,

,

,

,

,

,

**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**

**Solutions:**

**(a) **Line containing point E is

(b) Line passing through A is

(c) Line on which O lies is

(d) Two pairs of intersecting lines are

,

and

,

**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)**

(b)

**(c)**

(d)

**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**** 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 .**

**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**

**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

**(b) **The below figure is the closed curve

**3. Draw any polygon and shade its interior.**

**Solutions:**

The below figure is the polygon with interior shade

**4. Consider the given figure and answer the questions:**

**(a) Is it a curve?**

**(b) Is it closed?**

**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

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

(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.**

**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**

**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

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

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

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

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

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**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).