NCERT Solutions For Class 6 Maths Chapter 4 : Basic Geometrical Ideas (New Syllabus )

Complete NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas are given in the study circle. Practicing questions from NCERT Book Class 6 is important for the students who want to score the highest marks in their final exams. While solving the questions, students may face many difficulties. In study circle questions are solved in a very easy way.

All the students are provided with NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas as per CBSE syllabus by our experts to solve their queries.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Exercise 4.1

Question 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

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 - 5
and 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 - 10
and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 11

Question 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

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

Question 3. Use the figure to name:

(a) The line containing point E.
(b) The line passing through A.
(c) The line on which O lies
(d) Two pairs of intersecting lines.

NCERT Solutions for Class 6 Maths Chapter 4

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 - 30
and 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 4. How many lines can pass through

(a) one given point?
(b) two given points?

Solution :

(a) Countless lines can pass through one given point.
(b) One and only one line can pass through two given points.

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

(a) Point P lies on AB¯
(b) XY←→ and PQ←→ intersect at M.
(c) Line contains E and F but not D.
(d) Op¯ and OQ¯ meet at O.

NCERT Solutions for Class 6 Maths Chapter 4

NCERT Solutions for Class 6 Maths Chapter 4

NCERT Solutions for Class 6 Maths Chapter 4

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

. Say whether following statements are true or false in 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 segmentNCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 44

 .

(c) M and N are end points of line segmentNCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 45

.

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

.

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

.

(f) M is 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 rayNCERT 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 same as rayNCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 52
 .

(i) Ray NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 53

 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

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 Maths Chapter 4 Basic Geometrical Ideas

Exercise 4.2

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

NCERT Solutions for Class 6 Maths Chapter 4

Solutions:

(a) The given curve is an open curve

(b) The given curve is a closed curve

(c) The given curve is an open curve

(d) The given curve is a closed curve

(e) The given curve is a closed curve

2. Draw rough diagrams to illustrate the following:

(a) Open curve

(b) Closed curve

Solution:– (a) The below figure is an open curve

NCERT Solutions for Class 6 Maths Chapter 4

(b) The below figure is a closed curve

NCERT Solutions for Class 6 Maths Chapter 4

Question 3. Draw any polygon and shade its interior.

 

Class 6 Maths Chapter 4 Basic Geometrical Ideas

Question 4. Consider the given figure and answer the questions

(a) Is it a curve?

 

(b) Is it closed?

Class 6 Maths Chapter 4 Basic Geometrical Ideas

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.

Solution:–

Class 6 Maths Chapter 4 Basic Geometrical Ideas

(c) No, it’s not possible, as the polygon with the least number of sides is a triangle, which has three sides.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Exercise 4.3

Question 1. Name the angles in the given figure.

Class 6 Maths Chapter 4 Basic Geometrical Ideas

Solutions:

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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

Solutions:

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

(b) The points 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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

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

 

Class 6 Maths Chapter 4 Basic Geometrical Ideas

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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Exercise 4.4

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 the point A in its exterior or in its interior?

Solutions:

Point A lies on the given triangle ABC. It lies neither in the interior nor the exterior.

Class 6 Maths Chapter 4 Basic Geometrical Ideas

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 as common?

Class 6 Maths Chapter 4 Basic Geometrical Ideas

Solutions:

(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 as common.

 

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Exercise 4.5

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?

Solutions:

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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

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.

Solutions:  

Class 6 Maths Chapter 4 Basic Geometrical Ideas

(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 - 4
and 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 - 8
and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 9
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 10
or NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4. 5 - 11
NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 12
and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 13
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

Question 3. Investigate:

Use strips and fasteners to make a triangle and a quadrilateral. Try to push inward at any one vertex of the triangle. Do the same to the quadrilateral. Is the triangle distorted? Is the quadrilateral distorted? Is the triangle rigid? Why is it that structures like electric towers make use of triangular shapes and not quadrilaterals?

Solution :

On pushing inward at any one vertex of the triangle, the triangle is not distorted, However, the quadrilateral is distorted. Hence, a triangle is a rigid figure. This is why structures like electric towers make use of triangular shapes and not quadrilaterals.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Exercise 4.6

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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

Solutions:

(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

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

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

Solutions:

(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.

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

Solutions:

(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

Class 6 Maths Chapter 4 Basic Geometrical Ideas

 

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.

Solutions:

(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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