NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas
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Page 1
NCERT
SOLUTIONS
CLASS - 6TH
aglase .co
SOLUTIONS
CLASS - 6TH
aglase .co
Page 2
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
Class : 6th
Subject : Maths
Chapter : 4
Chapter Name : BASIC GEOMETRICAL IDEAS
Exercise 4.1
Q1 Use the �gure to name :
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Answer. (a) The �ve points are D, E, O, B AND C.
¯¯¯¯¯¯¯¯
(b) BD
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(c) OD, OB, OC, OE
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(d) DE, EO, OB, OC, BE
Page : 74 , Block Name : Exercise 4.1
Q2 Name the line given in all possible (twelve) ways, choosing only two letters at a time
from the four given.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Answer. AB, BC, CD, BA, CB, DC, AD, DA, AC, CA, BD, DB
Page : 74 , Block Name : Exercise 4.1
Page 1 of 11 Aglasem Schools
Class : 6th
Subject : Maths
Chapter : 4
Chapter Name : BASIC GEOMETRICAL IDEAS
Exercise 4.1
Q1 Use the �gure to name :
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Answer. (a) The �ve points are D, E, O, B AND C.
¯¯¯¯¯¯¯¯
(b) BD
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(c) OD, OB, OC, OE
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(d) DE, EO, OB, OC, BE
Page : 74 , Block Name : Exercise 4.1
Q2 Name the line given in all possible (twelve) ways, choosing only two letters at a time
from the four given.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Answer. AB, BC, CD, BA, CB, DC, AD, DA, AC, CA, BD, DB
Page : 74 , Block Name : Exercise 4.1
Page 1 of 11 Aglasem Schools
Page 3
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
Q3 Use the �gure to name :
(a) Line containing point E.
(b) Line passing through A.
(c) Line on which O lies
(d) Two pairs of intersecting lines.
¯¯¯¯¯¯¯¯
Answer. (a) AE
¯¯¯¯¯¯¯¯
(b) AE
¯¯¯¯¯¯¯¯
(c) OC
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯
(d) OC and AE, AE and EF
Page : 75 , Block Name : Exercise 4.1
Q4 How many lines can pass through (a) one given point? (b) two given points?
Answer. (a) In�nite number of lines can pass through a single point.
(b) Only one line can pass through two given points.
Page : 75 , Block Name : Exercise 4.1
Q5 Draw a rough �gure and label suitably in each of the following cases:
¯¯¯¯¯¯¯¯
(a) Point P lies on AB
¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(b) XY and P Q intersect at M.
(c) Line l contains E and F but not D.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯
(d) OP and OQ meet at O.
Answer. (a)
(b)
Page 2 of 11 Aglasem Schools
Q3 Use the �gure to name :
(a) Line containing point E.
(b) Line passing through A.
(c) Line on which O lies
(d) Two pairs of intersecting lines.
¯¯¯¯¯¯¯¯
Answer. (a) AE
¯¯¯¯¯¯¯¯
(b) AE
¯¯¯¯¯¯¯¯
(c) OC
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯
(d) OC and AE, AE and EF
Page : 75 , Block Name : Exercise 4.1
Q4 How many lines can pass through (a) one given point? (b) two given points?
Answer. (a) In�nite number of lines can pass through a single point.
(b) Only one line can pass through two given points.
Page : 75 , Block Name : Exercise 4.1
Q5 Draw a rough �gure and label suitably in each of the following cases:
¯¯¯¯¯¯¯¯
(a) Point P lies on AB
¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(b) XY and P Q intersect at M.
(c) Line l contains E and F but not D.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯
(d) OP and OQ meet at O.
Answer. (a)
(b)
Page 2 of 11 Aglasem Schools
Page 4
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
(c)
(d)
Page : 75 , Block Name : Exercise 4.1
¯¯¯¯¯¯¯¯¯¯¯
Q6 Consider the following �gure of line MN . Say whether following statements are true
or false in context of the given �gure.
¯¯¯¯¯¯¯¯¯¯¯
(a) Q, M, O, N, P are points on the line MN .
¯¯¯¯¯¯¯¯¯¯¯
(b) M, O, N are points on a line segment MN .
¯¯¯¯¯¯¯¯¯¯¯
(c) M and N are end points of line segment MN .
¯¯¯¯¯¯¯¯
(d) O and N are end points of line segment OP .
¯¯¯¯¯¯¯¯¯
(e) M is one of the end points of line segment QO .
¯¯¯¯¯¯¯¯
(f) M is point on ray OP .
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(g) Ray OP is different from ray QP .
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯
(h) Ray OP is same as ray OM .
¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(i) Ray OM is not opposite to ray OP .
¯¯¯¯¯¯¯¯
(j) O is not an initial point of OP .
Page 3 of 11 Aglasem Schools
(c)
(d)
Page : 75 , Block Name : Exercise 4.1
¯¯¯¯¯¯¯¯¯¯¯
Q6 Consider the following �gure of line MN . Say whether following statements are true
or false in context of the given �gure.
¯¯¯¯¯¯¯¯¯¯¯
(a) Q, M, O, N, P are points on the line MN .
¯¯¯¯¯¯¯¯¯¯¯
(b) M, O, N are points on a line segment MN .
¯¯¯¯¯¯¯¯¯¯¯
(c) M and N are end points of line segment MN .
¯¯¯¯¯¯¯¯
(d) O and N are end points of line segment OP .
¯¯¯¯¯¯¯¯¯
(e) M is one of the end points of line segment QO .
¯¯¯¯¯¯¯¯
(f) M is point on ray OP .
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(g) Ray OP is different from ray QP .
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯
(h) Ray OP is same as ray OM .
¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(i) Ray OM is not opposite to ray OP .
¯¯¯¯¯¯¯¯
(j) O is not an initial point of OP .
Page 3 of 11 Aglasem Schools
Page 5
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯
(k) N is the initial point of NP and NM .
Answer. (a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(i) False
(j) False
(k) True
Page : 75 , Block Name : Exercise 4.1
Exercise 4.2
Q1 Classify the following curves as (i) Open or (ii) Closed.
Answer. (a) Open
(b) Closed
(c) Open
(d) Closed
(e) Closed
Page : 78 Block Name : Exercise 4.2
Q2 Draw rough diagrams to illustrate the following :
Page 4 of 11 Aglasem Schools
¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯
(k) N is the initial point of NP and NM .
Answer. (a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(i) False
(j) False
(k) True
Page : 75 , Block Name : Exercise 4.1
Exercise 4.2
Q1 Classify the following curves as (i) Open or (ii) Closed.
Answer. (a) Open
(b) Closed
(c) Open
(d) Closed
(e) Closed
Page : 78 Block Name : Exercise 4.2
Q2 Draw rough diagrams to illustrate the following :
Page 4 of 11 Aglasem Schools
Page 6
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
(a) Open curve (b) Closed curve.
Answer. (a) Open curve
(b) Closed curve
Page : 78 Block Name : Exercise 4.2
Q3 Draw any polygon and shade its interior.
Answer.
Page : 78 Block Name : Exercise 4.2
Q4 Consider the given �gure and answer the questions : (a) Is it a curve? (b) Is it closed?
Answer. (a) Yes
(b) Yes
Page : 78 Block Name : Exercise 4.2
Exercise 4.3
Q1 Name the angles in the given �gure.
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(a) Open curve (b) Closed curve.
Answer. (a) Open curve
(b) Closed curve
Page : 78 Block Name : Exercise 4.2
Q3 Draw any polygon and shade its interior.
Answer.
Page : 78 Block Name : Exercise 4.2
Q4 Consider the given �gure and answer the questions : (a) Is it a curve? (b) Is it closed?
Answer. (a) Yes
(b) Yes
Page : 78 Block Name : Exercise 4.2
Exercise 4.3
Q1 Name the angles in the given �gure.
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Page 7
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
Answer. ∠BAD, ∠ADC, ∠DCB, ∠CBA
Page : 80 , Block Name : Exercise 4.3
Q2 In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of \angle \mathrm { EOF}
(c) On \angle \mathrm { EOF }
Answer. (a) A
(b) C, A, D
(c) B, E, O, F
Page : 80 , Block Name : Exercise 4.3
Q3 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)
∠COD and ∠AOB have point O in common.
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Answer. ∠BAD, ∠ADC, ∠DCB, ∠CBA
Page : 80 , Block Name : Exercise 4.3
Q2 In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of \angle \mathrm { EOF}
(c) On \angle \mathrm { EOF }
Answer. (a) A
(b) C, A, D
(c) B, E, O, F
Page : 80 , Block Name : Exercise 4.3
Q3 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)
∠COD and ∠AOB have point O in common.
Page 6 of 11 Aglasem Schools
Page 8
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
(b)
∠AOB and ∠BOC have points O and B in common.
(c)
∠AOB and ∠BOC have points O, E, B in common.
(d)
∠BOA and ∠COA have points O, E, D, A in common.
(e)
¯¯¯¯¯¯¯¯
Ray OC is common between ∠BOC and ∠AOC
Page : 80 , Block Name : Exercise 4.3
Exercise 4.4
Q1 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?
Answer.
Page 7 of 11 Aglasem Schools
(b)
∠AOB and ∠BOC have points O and B in common.
(c)
∠AOB and ∠BOC have points O, E, B in common.
(d)
∠BOA and ∠COA have points O, E, D, A in common.
(e)
¯¯¯¯¯¯¯¯
Ray OC is common between ∠BOC and ∠AOC
Page : 80 , Block Name : Exercise 4.3
Exercise 4.4
Q1 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?
Answer.
Page 7 of 11 Aglasem Schools
Page 9
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
Point A lies on the given ΔABC.
Page : 81 , Block Name : Exercise 4.4
Q2 (a) Identify three triangles in the �gure.
(b) Write the names of seven angles.
(c) Write the names of six line segments.
(d) Which two triangles have ∠B as common?
Answer. (a) We know that, a triangle is a three sided polygon. So, three triangles in the
given �gure are as follows:
(i) ΔABD (ii) ΔADC (iii) ΔABC
(b) An angle is made up of two rays starting from a common endpoint here the names of
seven angles are as follows:
(i) ∠BAD (ii) ∠BAC (iii) ∠CAD (iv)∠ABD (v) ∠ACD (vi) ∠ADC (vii) ∠ADB.
(c) The names of six line segments are as follow :
(i) AB (ii) BD (iii) DC (iv) CA (v) AD (vi) BC
(d) From the given �gure, it is clear that
∠B is common of ΔABD and ΔABC.
Page : 81 , Block Name : Exercise 4.4
Exercise 4.5
Q1 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?
Page 8 of 11 Aglasem Schools
Point A lies on the given ΔABC.
Page : 81 , Block Name : Exercise 4.4
Q2 (a) Identify three triangles in the �gure.
(b) Write the names of seven angles.
(c) Write the names of six line segments.
(d) Which two triangles have ∠B as common?
Answer. (a) We know that, a triangle is a three sided polygon. So, three triangles in the
given �gure are as follows:
(i) ΔABD (ii) ΔADC (iii) ΔABC
(b) An angle is made up of two rays starting from a common endpoint here the names of
seven angles are as follows:
(i) ∠BAD (ii) ∠BAC (iii) ∠CAD (iv)∠ABD (v) ∠ACD (vi) ∠ADC (vii) ∠ADB.
(c) The names of six line segments are as follow :
(i) AB (ii) BD (iii) DC (iv) CA (v) AD (vi) BC
(d) From the given �gure, it is clear that
∠B is common of ΔABD and ΔABC.
Page : 81 , Block Name : Exercise 4.4
Exercise 4.5
Q1 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?
Page 8 of 11 Aglasem Schools
Page 10
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
Answer.
Diagonals are PR and QS. They meet at point O which is in the interior of &mnSq1PQRS.
Page : 82 , Block Name : Exercise 4.5
Q2 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.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(a) KL, NM and KN, ML
(b) ∠KLM and ∠KNM
∠LKN and ∠LMN
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(c) KL, KN and NM, ML
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
KL, LM and NM, NK
(d) ∠K, ∠L and ∠M, LN
∠K, ∠N and ∠L, ∠M
Page : 82 , Block Name : Exercise 4.5
Page 9 of 11 Aglasem Schools
Answer.
Diagonals are PR and QS. They meet at point O which is in the interior of &mnSq1PQRS.
Page : 82 , Block Name : Exercise 4.5
Q2 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.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(a) KL, NM and KN, ML
(b) ∠KLM and ∠KNM
∠LKN and ∠LMN
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(c) KL, KN and NM, ML
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
KL, LM and NM, NK
(d) ∠K, ∠L and ∠M, LN
∠K, ∠N and ∠L, ∠M
Page : 82 , Block Name : Exercise 4.5
Page 9 of 11 Aglasem Schools
Page 11
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
Exercise 4.6
Q1 From the �gure, 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
Answer. (a) O
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(b) OA, OB, OC
¯¯¯¯¯¯¯¯
(c) AC
¯¯¯¯¯¯¯¯
(d) ED
(e) O, P
(f) Q
(g) AOB (shaded region)
(h) DE (shaded region)
Page : 84 , Block Name : Exercise 4.6
Q2 (a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?
Answer. (a) Yes. The diameter is the longest possible chord of the circle.
(b) No
Page : 84 , Block Name : Exercise 4.6
Q3 Draw any circle and mark
Page 10 of 11 Aglasem Schools
Exercise 4.6
Q1 From the �gure, 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
Answer. (a) O
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(b) OA, OB, OC
¯¯¯¯¯¯¯¯
(c) AC
¯¯¯¯¯¯¯¯
(d) ED
(e) O, P
(f) Q
(g) AOB (shaded region)
(h) DE (shaded region)
Page : 84 , Block Name : Exercise 4.6
Q2 (a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?
Answer. (a) Yes. The diameter is the longest possible chord of the circle.
(b) No
Page : 84 , Block Name : Exercise 4.6
Q3 Draw any circle and mark
Page 10 of 11 Aglasem Schools
Page 12
Book: Mathematics NCERT Solutions | Chapter - 4 Maths
(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.
(a) O
¯¯¯¯¯¯¯¯
(b) OA
¯¯¯¯¯¯¯¯
(c) AB
(d) COA
(e) DE
(f) O
(g) F
ˆ
(h) AC
Page : 84 , Block Name : Exercise 4.6
Q4 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. They will always intersect each other at the centre of the circle.
(b) True.
Page : 84 , Block Name : Exercise 4.6
Page 11 of 11 Aglasem Schools
(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.
(a) O
¯¯¯¯¯¯¯¯
(b) OA
¯¯¯¯¯¯¯¯
(c) AB
(d) COA
(e) DE
(f) O
(g) F
ˆ
(h) AC
Page : 84 , Block Name : Exercise 4.6
Q4 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. They will always intersect each other at the centre of the circle.
(b) True.
Page : 84 , Block Name : Exercise 4.6
Page 11 of 11 Aglasem Schools
Document Details
| Board / Org | NCERT |
| Exam | Class 6 |
| Type | Solution |
| Pages | 12 |
| Updated | 22 Jul 2026 |