NCERT Solutions Class 6 Maths Chapter 4 Basic Geometrical Ideas

Exercise 4.1: Types of Lines

In this exercise, students explore different types of lines, including intersecting, parallel, and perpendicular lines. Through various activities, they learn to identify and draw these lines. This exercise helps students understand how lines interact with each other and lays the groundwork for understanding more complex geometric structures.

Exercise 4.2: Polygons

This exercise of the chapter deals with polygons, teaching students to classify them based on the number of sides. Students learn to identify and draw a variety of polygons, such as triangles, quadrilaterals, pentagons, and hexagons. This exercise helps students develop an understanding of how different polygons are formed and their properties.

Exercise 4.3: Angles

The third exercise focuses on angles and their various types. Students learn to differentiate between acute, obtuse, right, straight, and reflex angles. They practice drawing and measuring angles using a protractor, which enhances their precision and understanding of angle measurement. This exercise is crucial for developing the skills to work with different geometrical shapes and figures.

Access NCERT Solutions for Class 6 Maths Chapter 4 – Basic Geometrical Ideas

Exercise: 4.1

1. Use the given figure to name:

a. Five points

Ans: A point denotes a location.

O, B, C, D, E are the five points.

b. A line

Ans: When the line segment from D to B is extended beyond D in one direction and beyond B in another direction, without any end, we get a line $\overleftrightarrow{DB}$

A line $\overleftrightarrow{DB}$

c. Four rays

Ans:  A portion of a line that starts at one point and goes endlessly in a direction is called a ray.

Rays are $OD,\:OE,\:OC,\:OB$

d. Five-line segments

Ans: The shortest join of two points represents a line segment.

Line segments are \[\overline {DE}, \overline {OE,} \overline {OC} ,\overline {OB} ,\overline {OD} \]

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

Ans: The shortest join of two points represents a line segment.

$\overline {AB} ,\overline {AC} ,\overline {AD} ,\overline {BC} ,\overline {BD} ,\overline {CD} ,\overline {BA} ,\overline {CA} ,\overline {DA} ,\overline {CB} ,\overline {DB} ,\overline {DC} $

3. Use the figure to name:

a. A line containing a point $E$

Ans: A line containing $E$ is $\overline {AE} $or $\overline {FE} $

b. Line passing through $A$

Ans: A line passing through $A$ is $\overline {AE} $

c. The line on which $O$ lies

Ans: A line on which $O$ lies is $\overline {OC} $

d. Two pairs of intersecting lines

Ans: If two lines have one common point, they are called intersecting lines.

Two pairs of intersecting lines are $\overline {AD} ,\overline {CO} $ and $\overline {AE} ,\overline {FE} $

4. How many lines can pass through: 

a. One point

Ans: An infinite number of lines. An infinite number of lines pass through point A.

b. Two given points

Ans: Consider the two points D and B. Only one line can pass through these two points.

Hence, through two given points only one line can pass.

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

a. Point P lies on $\overline {AB} $

Ans:

b. $\overline {XY}$ and $\overline {PQ}$ intersect at M.

Ans:

c. A line named ‘l’ contains E and F but not D

Ans:

d. OP and OQ meet at O

Ans:

6. Consider the following figure$\overline {MN} $. Identify if the given statements are true or false based on the given figure:

a. On the line, $\overline {MN} $, points are M, Q, O, N, P

Ans: True

A line consists of many points and a point determines a location. The line $\overline {MN} $ is obtained when points M, N are extended indefinitely on both sides. M, Q, O, N, P are hence the points on it.

b. The points on a line segment $\overline {MN} $ are M, O, N

Ans: True

The line segment represents the shortest join of two points. Here M, N are the endpoints of the line segment $\overline {MN} $ and we consider the point only till the endpoint of this segment $\overline {MN} $. So, M, O, N are the points.

c. M and N are endpoints of the line segment $\overline {MN} $

Ans: True

The line segment represents the shortest join of two points. Here M, N are the endpoints of the line segment $\overline {MN} $

d. O and N are endpoints of the line segment $\overline {OP} $

Ans: False

The line segment represents the shortest join of two points. For the line segment $\overline{OP}$, O and P, are endpoints.

e. M is one of the endpoints of the line segment $\overline {QO} $

Ans: False

For the line segment $\overline {QO} $, Q and O are the endpoints. The shortest join of two points is represented by a line segment.

f. Point M is a point on ray OP

Ans: False

A ray starts at a starting point and goes endlessly in a direction. For the ray OP, O is the starting point and the direction of the ray is towards P. M is hence not a point on ray OP.

g. Ray QP is different from ray OP

Ans: True

For the ray QP, Q is the starting point and for the ray OP, O is the starting point. So, both these rays are different.

h. Ray OP same as ray OM

Ans: False

A ray starts at a starting point and goes endlessly in a direction. For the ray OP and OM, though the starting points are the same, the direction of both rays is different.

i. The ray OM is not opposite to the ray OP.

Ans: False

For the ray OP and OM, the starting point is O. But the direction of ray OM is towards M, and the direction of OP is towards P. These points are on the same line and the ray OM is opposite to ray OP.

j. The initial point of $\overline {OP} $ is not O.

Ans: False

For the line segment $\overline{OP}$, O and P are the two endpoints and O is the initial point.

k. Point N is the initial point of  $\overline {NP} $ and $\overline {NM} $

Ans: True

The line segment represents the shortest join of two points. For both of the line segments $\overline{NP}$ and $\overline{NM}$, N is the initial point.

Exercise: 4.2

1. Classify the following curves as ‘Open’ or ‘Closed’

a. 

Ans: Open

b. 

Ans: Closed

c. 

Ans: Open

d. 

Ans: Closed

e. 

Ans: Closed

2. Draw rough diagrams to illustrate the following:

a. Open curve

Ans:

b. Closed curve

Ans:

3. Draw any polygon and also shade its interior.

Ans: Polygon ABCDE

4. Consider the given figure and answer the questions:

a. Is it a curve?

Ans: Ye

b. Is it closed?

Ans: Yes

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

a. Draw a closed curve that is not a polygon.

Ans:

b. Draw an open curve that is made up entirely of line segments.

Ans:

c. A polygon with two sides.

Ans: A polygon having two sides is impossible.

Exercise: 4.3

1. Name the angles in the given figure:

Ans: Starting from a common starting point, an angle is made up of two rays. So, here 

$\angle ABC,\angle CDA,\angle DAB,\angle DCB$ are the names of angles.

2. In the given diagram, name the point(s):

a. In the interior of $\angle DOE$ 

Ans: A given angle can lead to three divisions of a region. The region on the angle, the region interior of angle, and region exterior of angle. The points interior of the angle $\angle DOE$ is the interior points.

Point interior of $\angle DOE$ is A

b. In the exterior of $\angle EOF$

Ans:   Region exterior of the angle $\angle EOF$ is the exterior region and points in this region are exterior points.

Points exterior of $\angle EOF$ are C, A, D

c. On $\angle EOF$

Ans: A given angle can lead to three divisions of a region and some of the points may be located on the angle.Points on $\angle EOF$ are E, B, O, F

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

a. One point in common

Ans:

$\angle AOB$ and $\angle DOC$ have O as their common point.

b. Two points in common

Ans:

$\angle ABC$ and $\angle CBE$ has B and C as their two common points.

c. Three points in common

Ans:

$\angle ABC$ and $\angle CBE$ have B, D, C as their three common points.

d. Four points in common

Ans:

$\angle ABC$ and $\angle CBE$ have B, F, D, C as their four common points.

e. One ray in common

Ans:

$\angle AOB$ and $\angle AOC$ has the ray $\overline {AO} $in common.

Overview of Deleted Syllabus for CBSE Class 6 Maths Basic Geometrical Ideas

Class 6 Maths Chapter 4: Exercises Breakdown

Conclusion

In Basic Geometrical Ideas Class 6 students explore the fundamental concepts of geometry, which form the building blocks for more advanced mathematical studies. This chapter covers various topics, including Point, Line, Line Segment, and Ray, Open and Closed Figures, Curves, Polygons, Angles and Triangles, and Circles. In previous years' exams, an average of 3-5 questions have been asked from this chapter. These questions typically include identifying and describing geometrical shapes, drawing and labeling basic geometrical figures, and understanding their properties. Keep practicing the questions from Basic Geometrical Ideas Class 6 PDF to excel in your exams.

Other Study Material for CBSE Class 6 Maths Chapter 4

Chapter-Specific NCERT Solutions for Class 6 Maths

Given below are the chapter-wise NCERT Solutions for Class 6 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.