Class 6 Maths Chapter 4 Basic Geometrical Ideas
Directions: In each of the questions 1 to 5, out of four options only one is correct. Write the correct answer.
1. The number of lines passing through five points such that no three of them are collinear is
(1) 10
(2) 5
(3) 20
(4) 8
Solution: (1) : Since, total number of points is 5 and we need two points to form a line.
Total number of lines passing through the points is 5 x 2 = 10
2. The number of diagonals in a septagon is
(1) 21
(2) 42
(3) 7
(4) 14
Solution: (4): Since, the number of diagonals in
a polygon =n(n-3)/2
Septagon has 7 sides, i.e., n = 7
The number of diagonals in a septagon
Read and Learn More Class 6 Maths Exemplar Solutions
3. Number of line segments in figure is
(1) 5
(2) 10
(3) 15
(4) 20
Solution: (2) : The adjacent figure shows the line segments;
AB, BC, CD, AC, AD, BD, AE, BE, CE, DE
Thus, there are 10 line segments.
4. The number of angles in the given figure is
(1) 3
(2) 4
(3) 5
(4) 6
Solution: (4): The names of angles formed in the given figure are ZAOB, ZAOC, ZAOD, ZBOC, ZBOD, and ZCOD.
There are a total of 6 angles formed.
5. A polygon has a prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is
(1) 4
(2) 5
(3) 7
(4) 10
Solution: (2): We have given, the number of sides of a polygon
= Sum of the two least consecutive primes
= 2 +3 =5 [ ∴ 2 and 3 are the least consecutive prime numbers]
The number of diagonals = n(n- 3)/2
where n = 5
=5(5-3)/2=5×2/2=5
Directions: In questions 6 to 14, fill in the blanks to make the statements true
6. The number of diagonals in a hexagon is
Solution: 9 : Number of diagonals = n(n-3)/2
where n = 6
=6(6-3)/2=6×3/2=9
7. In the given figure, points lying in the interior of the triangle PQR are_________, that in the exterior are__________ and that on the triangle itself are__________.
Solution: O and S; T and N; P, Q, R and M
8. In the given figure, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then
(1) AD=AB +________
(2) AD=AC +_________
(3) midpoint of AE is_____________
(4) midpoint of CE is__________
(5) AE=_______x AB
Solution: (1) BD: AD=AB + BC + CD=AB + BD
(2) CD:AD = AB + BC+CD=AC + CD
(3) C: AB + BC = CD + DE
=> AC = CE :. Mid point of AE is C.
(4) D : CD = DE
Mid point of CE is D.
(5) 4 : AB + BC + CD + DE = AE
=> AB+AB+AB + AB = AE ∴ 4AB = AE
9. The number of straight angles in given figure is____________.
Solution: 4: The number of straight angles in the given figure is 4.
10. The number of common points in the two angles marked in the given figure is_______.
Solution: Two: The two angles marked; ∠PAQ and ∠PDQ.
The number of common points are 2 and these are P and Q.
11. The number of common points in the two angles marked in a given figure is__________.
Solution: One: The two angles marked; ∠CAB and ∠DAE.
The number of common points is 1 and that is A.
12. The number of common points in the two angles marked in given figure _________.
Solution: Three: There are 3 common points in the two angles marked in the given figure and these are P, Q, and R.
13. The number of common points in the two angles marked in a given figure is_______.
Solution: Four: The number of common points in the two angles marked in the given figure is 4 and these are E, D, G and F.
14. The common part between the two angles BAC and DAB in given figure is_____.
Solution: Ray AB
Directions: State whether the statements given in questions 15 to 21 are true (T) or false (F).
15. If line PQ|| line m, then line segment PQ || m.
Solution: True
16. Two parallel lines meet each other at some point.
Solution: False
Two lines in a plane which do not meet even when produced indefinitely in either direction, are known as parallel lines.
17. Measures of ∠ABC and ∠CBA in given figure are the same.
Solution: True
ABC is same as ∠CBA.
18. Two line segments may intersect at two points.
Solution: False
The intersecting point of any two line segments is only one.
19. Many lines can pass through two given points.
Solution: False
There is only one line which passes through two given points.
20. Only one line can pass through a given point.
Solution: False
There are infinite number of lines which passes through a given point.
21. Two angles can have exactly five points in common.
Solution: False
It can have any number of points.
22. Name all the line segments in given figure.
Solution: The line segments are AB, BC, CD, DE, AC, AD, AE, BD, BE and CE
23. Name the line segments shown in given figure
Solution: The line segments are AB, BC, CD, DE and EA
24. State the mid points of all the sides of given figure.
Solution: X is a mid-point of AC,
Y is a mid-point of BC and
Z is a mid-point of AB.
25. Name the vertices and the line segments in given figure.
Solution: The vertices are : A, B, C, D and E.
The line segments are : AB, BC, CD, DE, EA, AC and AD.
26. Name the following angles of given figure,using three letters :
(1) ∠1
(2) ∠2
(3) ∠3
(4) ∠1+∠2
(5) ∠2 + ∠3
(6) ∠1+∠2 + ∠3
(7) ∠CBA-∠1
Solution:(1) ∠1 = ∠CBD
(2) ∠2 = ∠DBE
(3) ∠3 = ∠EBA
(4) ∠1 +∠2 = ∠CBD + ∠DBE = ∠CBE
(5) ∠2 + ∠3 = ∠DBE +vEBA = ∠DBA
(6) ∠1 + ∠2 + ∠3 = ∠CBD + ∠DBE + ∠EBA = ∠CBA
(7)∠CBA- ∠1 = ∠CBA- ∠CBD = ∠DBA
27. Name the points and then the line segments in each of the following figures:
Solution:(i) Name of the points -> A,B and C.
Name of the line segments —> AB, BC and CA.
(ii) Name of the points —>A,B,C and D.
Name of the line segments —> AB, BC, CD and DA.
(iii) Name of the points —> A, B, C, D and E.
Name of the line segments —> AB, BC, CD, DE, and EA.
(iv) Name of the points —> A, B, C, D, E and F.
Name of the line segments —> AB, CD and EF.
28. Which points in given figures, appear to be mid-points of the line segments? When you locate a mid-point, name the two equal line segments formed by it.
Solution:(i) The given figure shows there is no mid-point.
(ii) The given figure shows that O is the mid-point of AB and the name of the two equal line segments are AO and OB.
(iii) The given figure shows that D is the mid-point of BC and the name of the two equal line segments are BD and DC.
29. Find out the incorrect statement, if any, in the following : An angle is formed when we have
(1) two rays with a common end-point
(2) two line segments with a common endpoint
(3) a ray and a line segment with a common end-point
Solution: All the three statements (1), (2) and (3) are incorrect.
The common initial point of two rays forms an angle.
30. What is common in the following figures (i) and (ii)? Is figure (i) that of triangle? if not, why?
Solution: Both the figures (i) and (ii) have 3 line segments.
No, Fig. (i) is not a triangle since the three line segments does not form a closed figure.
31. If two rays intersect, will their point of intersection be the vertex ofan angle of which the rays are the two sides?
Solution: Yes
32. How many points are marked in given figure?
Solution: Two points A and B are marked
33. How many line segments are there in given figure?
Solution: Only one line segment, AB is there.
34. In given figure, how many points are marked? Name them.
Solution: From the given figure, Three points A, B, and C are marked.
35. How many line segments are there in the given figure? Name them.
Solution: From the given figure, Three line segments, namely AB, BC, and AC are there.
36. In the given figure, how many points are marked? Name them.
Solution: From the given figure, Four points A, B, C, and D are marked.
37. In the given figure how many line segments are there? Name them.
Solution: Six line segments, namely AB, AC, AD, BC, BD, and CD.
38. In the given figure, how many points are marked? Name them
Solution: From the given figure, Five points are marked, namely A, B, D, E and C.
39. In given figure how many line segments are there? Name them
Solution: From the given figure, Ten line segments, namely AB, AD, AE, AC, BD, BE, BC, DE, DC and EC.
40. In given figure,O is the centre of the circle.
(1) Name all chords of the circle.
(2) Name all radii of the circle.
(3) Name a chord, which is not the diameter of the circle.
(4) Shade sectors OAC and OPB.
(5) Shade the smaller segment of the circle formed by CP.
Solution:(1) Name of chords : PC and BA.
(2) Name of radii : PO, OC, OB and OA.
(3) PC is a chord which is not the diameter of the circle
(4) 
(5) 
41. Write the name of
(1) vertices
(2) edges, and
(3) faces of the prism shown In given figure.
Solution: (1) Vertices: A, B, C, D, E and F.
(2) Edges: AB, BC, AC, DF, FC, BD. EF, ED and AE.
(3) Faces: EACF, EDBA, ABC, DEF and DBCF.
42. How many edges, faces and vertices are there in a sphere?
Solution: In a sphere, edges – 0, faces – 0 and vertices- 0.
43. Draw all the diagonals of a pentagon ABCDE and name them.
Solution: The diagonals of a pentagon ABCDE are AC, AD, BE, BD and EC.
