NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

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ncert solutions for class 6 maths Chapter 4

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 - 3NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 4NCERT 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 - 7NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 8NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 9NCERT 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 - 13NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 14NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 15NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 16NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 17NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 18NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 19NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 20NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 21NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 22NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 23NCERT 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 - 29NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 30and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.1 - 31NCERT 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 suitably in each of the following cases:

(a) Point P lies onNCERT 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.

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 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 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 the same as ray.

(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 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

Solutions:

(a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True


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 an 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 a 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 it’s not possible, as the polygon having the least number of sides is a triangle that has three sides.


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 common ray between ∠BOC and ∠AOC

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


Exercise 4.4

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?

Solutions:

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

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

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?

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

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 - 4NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 5NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 6NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 7NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.4 - 8

(d) ∠ABD and ∠ABC are triangles that have ∠B as common.


Exercise 4.5

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.

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

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:

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 - 3NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 4and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 5NCERT 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 - 7NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 8 and, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 10 or, NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 12and NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 - 13NCERT 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


Exercise 4.6 page no: 84

1. From the figure, identify:

(a) the centre of the 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

Solutions:

(a) The centre of the circle is O

(b) Three radii are NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 2NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.6 - 3NCERT 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. Diameter is also called as a longest chord.

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

3. Draw any circle and mark

(a) it’s 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:

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

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.

 

 


 

  • Chapter 1 Knowing our Numbers
  • Chapter 2 Whole Numbers
  • Chapter 3 Playing With Numbers
  • Chapter 4 Basic Geometrical Ideas
  • Chapter 5 Understanding Elementary Shapes
  • Chapter 6 Integers
  • Chapter 7 Fractions
  • Chapter 8 Decimals
  • Chapter 9 Data Handling
  • Chapter 10 Measurement And Mensuration
  • Chapter 11 Algebra
  • Chapter 12 Ratio Proportion
  • Chapter 13 Introduction To Symmetry
  • Chapter 14 Practical Geometry Application

 

 

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