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NCERT solutions for class 6 maths chapter4 Basic Geometrical Ideas

NCERT Solutions for Class 6 Maths offer comprehensive explanations for the questions found within the NCERT textbooks endorsed by the Central Board of Secondary Education (CBSE). Orchids the international school provides these NCERT Class 6 Maths Solutions on a chapter-by-chapter basis, aiming to assist students in resolving any uncertainties and acquiring a profound comprehension of the subject matter. These resources, including NCERT Solutions, are conveniently accessible in PDF format, allowing students to download them for offline learning.

NCERT Solutions for Maths Basic Geometrical Ideas

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Access Answers to NCERT solutions for class 6 maths chapter4 Basic Geometrical Ideas

Introduction

Question 1 :

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

 

Answer :

(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

 


Question 2 :

 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

Answer :

(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

 


Question 3 :

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

Answer :

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

 


Question 4 :

 How many lines can pass through

(a) one given point?

 

(b) two given points?

 

Answer :

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

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

 


Question 5 :

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

 

(a) Point P lies on NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 33 .

 

 

(b) NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 34 and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 35 intersect at M.

 

 

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

 

 

(d) NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 36 and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 37 meet at O.

 

Answer :

(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


Question 6 :

Consider the following figure of line NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 42. 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 NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 43.

(b) M, O, N are points on a line segment NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 44 .

(c) M and N are the endpoints of the line segment NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 45.

(d) O and N are the endpoints of the line segment NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 46.

(e) M is one of the endpoints of the line segment NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 47.

(f) M is the point on ray NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 48.

(g) Ray
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 49 is different from ray NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 50 .

(h) Ray NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 51 is the same as ray NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 52 .

(i) Ray is not opposite to ray NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 54.

(j) O is not an initial point of NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 55

(k) N is the initial point of NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 56 and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 57.

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

 

Answer :

(a) True

 

 

(b) True

 

 

(c) True

 

 

(d) False

 

 

(e) False

 

 

(f) False

 

 

(g) True

 

 

(h) False

 

 

(i) False

 

 

(j) False

 

 

(k) True


Points

Question 1 :

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

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

 

 

Answer :

(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

 


Question 2 :

 Draw rough diagrams to illustrate the following:

(a) Open curve

(b) Closed curve

 

Answer :

(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


Question 3 :

Draw any polygon and shade its interior.

 

Answer :

The below figure is the polygon with interior shade

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

 

 


Question 4 :

 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.

 

Answer :

(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.

 








 


Question 5 :

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

Answer :

(a) Yes, it is a curve

(b) Yes, it is a closed curve

 


A Line Segment

Question 1 :

Name the angles in the given figure.

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

 

 

Answer :

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

 


Question 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

 

 

Answer :

(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

 


Question 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

 

Answer :

(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

 

 


A line

Question 1 :

Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is point A in its exterior or in its interior?

 

Answer :

Point A lies on the given triangle ABC, as shown below. It lies neither in interior nor exterior.

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 1


Question 2 :

(a) Identify three triangles in the figure.

(b) Write the names of seven angles.

(c) Write the names of six line segments

(d) Which two triangles have ∠B in common?

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 2

Answer :

(a) The three triangles are ∠ABD, ∠ACB, ∠ADC

(b) The angles are ∠BAC, ∠BAD, ∠CAD, ∠ADB, ∠ADC, ∠ABC, ∠ACB

(c) The line segments are NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 3, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 4, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 5, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 6, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 7, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 8

(d) ∠ABD and ∠ABC are triangles which have ∠B in common.

 


Intersecting Lines

Question 1 :

 Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?

 

Answer :

PR and QS are the diagonals. They meet at point O, which is in the interior of the quadrilateral.

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 1


Question 2 :

 Draw a rough sketch of a quadrilateral KLMN. State,

(a) two pairs of opposite sides,

(b) two pairs of opposite angles,

(c) two pairs of adjacent sides,

(d) two pairs of adjacent angles.

 

Answer :

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 2

(a) Two pairs of opposite sides are NCERT Solutions for Class 6 Matha Chapter 4 Exercise 4.5 - 3, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 4and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 5, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 6

(b) Two pairs of opposite angles are ∠KLM, ∠KNM and ∠LKN, ∠LMN

(c) Two pairs of adjacent sides are
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 7, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 8and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 9, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 10or NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4. 5 - 11, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 12and , NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 14

(d) Two pairs of adjacent angles are ∠K, ∠L and ∠M, ∠N or ∠K, ∠L and ∠L, ∠M

 


Parallel Lines

Question 1 :

 From the figure, identify:

(a) the centre of circle

(b) three radii

(c) a diameter

(d) a chord

(e) two points in the interior

(f) a point in the exterior

(g) a sector

(h) a segment

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 1

 

 

Answer :

(a) The centre of the circle is O

(b) Three radii are NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 2, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 3, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 4

(c) A diameter is NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 5

(d) A chord is NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 6

(e) Two points in the interior are O and P

(f) A point in the exterior is Q

(g) A sector is AOB, i.e. shaded region

(h) A segment is ED, i.e. shaded region

 


Question 2 :

 (a) Is every diameter of a circle also a chord?

(b) Is every chord of a circle also a diameter?

 

Answer :

(a) Yes, every diameter of a circle is also a chord. The diameter is also called the longest chord.

(b) No, every chord is not a diameter.

 


Question 3 :

Draw any circle and mark

(a) its centre

(b) a radius

(c) a diameter

(d) a sector

(e) a segment

(f) a point in its interior

(g) a point in its exterior

(h) an arc

 

Answer :

NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 7

(a) The centre of the circle is O.

(b) The radius is OC

(c) A diameter is NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 8

(d) A sector is AOC

(e) A segment is DE

(f) A point in its interior is O

(g) A point in its exterior is F

(h) An arc is NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 9

 


Question 4 :

 Say true or false:

(a) Two diameters of a circle will necessarily intersect.

(b) The centre of a circle is always in its interior.

 

Answer :

(a) True, two diameters will always intersect each other at the centre of the circle.

(b) True, the centre of the circle will always be in its interior.






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