Important Questions for CBSE Class 6 Maths Chapter 4 – Basic Geometrical Ideas

Class 6 Maths Chapter 4 Important Questions – Basic Geometrical Ideas

Maths is an important subject that students study in school, and we require Maths in our daily life. Chapter 4 of Class 6 Maths under CBSE curriculum discusses basic geometric ideas. Geometry is an important branch of Maths.

In Chapter 4, students will learn the basic components of geometry, i.e., point, line, curve and polygon. They will learn about different shapes, such as triangles, quadrilaterals, circles etc. It is a very important chapter because students will greatly need geometry in later classes. So, they must build their concepts clearly and have no doubts. They must practise questions from this chapter to score better in exams.

Extramarks is a leading educational company that provides different study materials related to CBSE and NCERT. Our experts have made the Important Questions Class 6 Maths Chapter 4 for students. They have included several types of questions from various sources such as the textbook exercise, NCERT exemplar, CBSE sample papers and CBSE past years’ question papers. 

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Basic Geometrical Ideas Class 6 Questions and Answers

The experts of Extramarks have collected these questions from sources like the textbook exercise, CBSE sample papers, NCERT exemplars and important reference books. They have also included a few questions from CBSE past years’ question papers so that students may know which type of questions come in exams. They have also given solutions to the following questions. Thus, the Important Questions Class 6 Maths Chapter 4 will help students to score better in exams. The questions are-

Question 1. A _____ has only one endpoint.

Answer 1. ray 

(A ray has only one fixed point.)

Question 2. _____ line/s can be drawn passing through two given points.

Answer 2. One 

(Only 1 line can be drawn from two fixed points.)

 Question 3. A quadrilateral is a polygon which is formed by _____ line segments.

Answer 3. four 

(A quadrilateral consists of 4 sides.)

 Question 4. _____ is the largest chord.

Answer 4. diameter 

(A chord is said to be a line which has both its end present in the circumference and diameter is said to be the longest chord as it passes through the centre.) 

 Question 5. A _____ of the circle is a line segment having one endpoint in the centre and the other endpoint on the circumference.

Answer 5. radius 

(It is the total distance between the centre and the circumference.) 

Question 6. Fill up the following:

• ________ has no length, breadth, height or thickness.

• A line segment has a definite ___________ .

• Curves that do not intersect within themselves are called ___________ curves.

• An ‘angle’ is made up of ___________ rays having a common endpoint.

Answer 6. 

1. Point
2. length
3. simple
4. two

Question 7. Classify the following given curves as (i) open or (ii) closed.

Answer 7. 

1. The given curve is an open curve.
2. The given curve is a closed curve.
3. The given curve is an open curve.
4. The given curve is a closed curve.

Question 8. Draw a rough diagram to illustrate the following:

(a) Open curve

(b) Closed curve

Answer 8. 

We will use the concept knowledge of open and closed shapes to answer the given question.

(a) Open curve: Open shapes are not continuous and are made up of line segments or curves which do not meet.

(b) Closed curve: Any enclosed shape that has no open ends and can be traced back from where it started without any break is known as a closed curve.

Question 9. Illustrate each one of the following given points – 

(a) A closed curve that is not any polygon.

(b) Open curve made up entirely of different line segments.

(c) A polygon containing two sides.

Answer 9. 

(a) The closed curves can be traced without any break. Closed curves start and end in the same place simultaneously. 

(b) Open curves are not continuous and are mostly made up of line segments or curves which do not meet or intersect.

(c) A polygon is mostly defined as a closed two-dimensional figure containing three or more straight lines. The smallest polygon that exists is a triangle having three sides. Thus, a polygon with two sides does not exist. 

Question 10. Consider the given figure below and answer the following questions.

(a) Does it represent a curve?

(b) Is its shape closed?

Answer 10.

By definition, a curve is a shape, or a line smoothly drawn in a plane, and it may have bents or turns. 

We will use the concept of open and closed shapes.

Open curves are not continuous. They are made up of line segments or curves which do not meet. They can be traced without any break. 

Closed curves start and end in the same place.

Yes, the figure given above is a curve. Yes, it is a curve-closed curve because all the lines are connected with each other.

Question 11. Write down how many lines can pass through

(a) one given point.

(b) two given points.

Answer 11.

We use the concepts of points and lines.

A line is a figure made when two points are connected with each other and have a minimum distance between them, and both ends are extended to infinity.

A point is defined as the location in any space and is represented by the dot (.) symbol. It does not have length, height, shape, or size.

(a) An infinite number of lines can pass through one point.

(b) Only one unique line passes through two given points.

Question 12. Match the following:

(a) Triangle (1) 4 sides

(b) Quadrilateral (2) 8 sides

(c) Heptagon (3) 3 sides

(d) Pentagon (4) 5 sides

(e) Octagon (5) 7 sides

(f) Hexagon (6) 6 sides                       

Answer 12.

(a)−(3)

−(3) A triangle is a polygon with three sides.

(b)−(1)

−(1) A quadrilateral is a polygon with four sides.

(c)−(5)

−(5) A heptagon is a polygon with seven sides.

(d)−(4)

−(4) A pentagon is a polygon with five sides.

(e)−(2)

−(2) An octagon is a polygon with eight sides.

(f)−(6)

−(6) A hexagon is a polygon with six sides.

Question 13. Use the following figure to name:

(a) five points

(b) a-line

(c) four rays

(d) five line segments

Answer 13.

(a) A point is the location in any space and is represented by a dot (.) symbol. It does not have length, height, shape, or size. The five points are O, B, C,D, and E.

(b) The length of the line is undefined. It can have infinite numbers of points. Therefore, the line is BD.

(c) A ray is the part of a line with only one fixed point, and the other point does not have any end. So the four rays are OC, OB, OE, and OD.

(d) It is the path present between the two points with a definite length that can be measured easily. Five line segments present are OE, ED, OD, OB, and EB.

Question 14. In the given diagram below, name the points(s)

(a) in the interior of  angle ∠DOE

(b) in the exterior of angle ∠EOF

(c) on angle ∠EOF

Answer 14.

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

(b) The point present in the exterior of ∠EOF is C, A and D.

(c) The points present on the angle ∠EOF are E, B, O and F.

Question 15. Draw rough diagrams of any two angles such that they contain

(a) one point which is common

(b) two points which is common

(c) three points which is common

(d) four points which is common

(e) one ray which is common

Answer 15.

(a) O is the common point between angles ∠COD and ∠AOB.

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

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

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

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

Question 16. Draw a rough sketch of any quadrilateral KLMN. State the following: 

(a) two pairs of opposite sides present in them. 

(b) two pairs of opposite angles present in them. 

(c) two pairs of adjacent sides present in them. 

(d) two pairs of adjacent angles present in them. 

Answer 16.

(a) Two pairs of opposite sides are – KL, NM and KN, ML.

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

(c) Two pairs of adjacent sides are – KL, KN and NM, ML or KL, LM and NM, NK.

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

Question 17. From the figure, identify the following:

(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.

Answer 17.

(a) The centre of the circle is O.

(b) Three radii are OA, OB and OC. 

(c) The diameter is AC.

(d) A chord is ED

(e) 2 points in the interior are O and P.

(f) A point in the exterior is Q.

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

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

Question 18. 

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

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

Answer 18.

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

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

Question 19. Draw any circle and mark the following:

(a) the centre of the circle 

(b) a radius of the circle 

(c) a diameter of the circle 

(d) a sector of the circle 

(e) a segment of the circle 

(f) a point in its interior of the circle 

(g) a point in its exterior of the circle 

(h) an arc

Answer 19.

(a) The centre of the circle is O.

(b) A radius is OC.

(c) The diameter is AB.

(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 AC. 

Question 20. State true (T) or false (F):

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

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

Answer 20.

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

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

Question 21. State if the following sentences are true or false.

1. a) A vertical line and a horizontal line always intersect at right angles.
2. b) If the arms of an angle on the paper are increased, the angle increases.
3. c) If the arms of an angle on the paper are decreased, the angle decreases.
4. d) If line PQ || line m, then line segment PQ || m.
5. e) Two parallel lines meet each other at some point.

Answer 21.

1. a) True.
2. b) False. The angle is not affected when the arms of an angle present on the paper are increased or decreased.
3. c) False. The angle is not affected when the arms of an angle present on the paper are increased or decreased.
4. d) True. From the question, line PQ is parallel to line m.

So, parts of those lines are also parallel.

Therefore, line segment PQ is parallel m.

1. e) False. Parallel lines never meet each other.

Question 22. The number of right angles present in a straight angle is ______, and the number of right angles present in a complete angle is ______.

Answer 22.

The number of right angles present in a straight angle is two, and that in a complete angle is four.

We know that the angle formed by a straight angle = is 180 degrees.

and angle formed by right angle = 90 degrees

So, the number of right angles = 180/90= 2

We know that complete angle = 360 degrees.

So, the number of right angles = 360/90= 4

Question 23.

a) Two line segments may intersect at 2 points.

b) Many lines can pass through 2 given points.

c) Only 1 line can pass through a given point.

d) 2 angles can have exactly five points in common.

Answer 23.

1. a) False. Because two line segments intersect at only one point.
2. b) False. Only 1 line can pass through two given points.
3. c) False. An infinite number of lines can pass/cross through the given point.
4. d) False. Two angles can only have either one or two five points in common.

Question 24. The number of lines of symmetry in a scalene triangle is

(A) 0

(B) 1

(C) 2

(D) 3

Answer 24.

(A) A scalene triangle has no/zero line of symmetry.

Question 25.

The number of lines of symmetry present in the circle is

(A) zero

(B) two

(C) four

(D) more than 4

Answer 25.

(D) Since a circle is symmetrical about each of its diameters. Thus, each diameter of a circle is an axis of symmetry.

Question 26. Draw a rough sketch of any quadrilateral PQRS. Draw its diagonals. Name them as well. Is the meeting point of all the diagonals present in the interior or in the exterior of the quadrilateral?

Answer 26.

A quadrilateral is a closed shape figure that is formed by joining the four points, among which any 3 points are non-collinear. 

The sketch of quadrilateral PQRS is shown below. Clearly, the meeting point of both the diagonals SQ and PR, which is O, is in the interior of the quadrilateral PQRS.

Question 27. 

(a) Identify any three triangles in the figure.

(b) Write the names of all the seven angles present in the figure.

(c) Write the names of all the six line segments.

(d) Which of the two triangles has ∠B in common?

We use the concept of knowledge of angles and triangles to answer the given question.

1. The three triangles can be identified as Δ ABD, Δ ADC and Δ ABC.
2. The seven angels are ∠ABD, ∠BDA, ∠ADC, ∠DCA, ∠CAB, ∠CAD and ∠DAB
3. The six-line segments are AB, AC, BC, BD, DC and AD.
4. Δ ABD and Δ ABC have ∠B in common.

Question 28. Draw a sketch of a triangle ABC. Mark point P in its interior and point Q in its exterior. Is point A present in its exterior or in its interior?

Answer 28.

We use the concept knowledge of triangles to answer the given question.
A triangle ABC has been drawn and points P and Q have been marked in their interior and exterior, respectively.

Point A is a vertex of the triangle ABC. It is neither in its exterior nor in its interior.

Question 29. Consider the given figure of line MN. State whether the statements written below are true or false in the context of the following figure.

(a) Q, M, O, N, and P are the points present on the line MN.

(b) M, O, and N are the points on a line segment MN.

(c) Are M and N the endpoints of line segment MN?

(d) Are O and N the endpoints of line segment OP?

(e) M is one of the endpoints of the line segment QO.

(f) M is the point on ray OP.

(g) Ray OP is different from the ray QP.

(h) Ray OP is different from the ray OM.

(i) Ray OM is not opposed to the ray OP.

(j) Is O not an initial point of OP? 

(k) Is N the initial point of NP and NM?

Answer 29.

We use the concept of points and lines to answer this given question.

(a) Q, M, O, N, and P are the points on the line MN is a true statement. 

(b) M, O, and N are the points on the line segment. MN is a true statement.

(c) M and N are the endpoints of the line segment. MN is a true statement.

(d) O and N are the endpoints of the line segment OP is a false statement.

(e) M is one of the endpoints of the line segment QO is a false statement. 

(f) M is the point on ray OP is a false statement.

(g) Ray OP is different from the ray QP and is a true statement.

(h) Ray OP is different from ray OM is a false statement. 

(i) Ray OP is not opposed to ray OM, this is a false statement. 

(j) O is not the initial point of OP, hence this is a false statement.

(k) N is the initial point of NP and NM, this is a true statement. 

Question 30. State true(T) or false(F).

(a) Two lines are called parallel in nature if they do not intersect, even when produced.

(b) Two parallel lines are everywhere with the same distance separating them.

(c) If two line segments do not meet or intersect, then these line segments are parallel.

(d) If two rays do not intersect, then they are parallel in nature.

(e) A line between two parallel lines is always said to be perpendicular. 

Answer 30.

(a) True

(b) True

(c) True

(d) True

(e) True

Benefits of Solving Basic Geometrical Ideas Class 6 Extra Questions

Practising is an important key to success. Students must practise as much as possible to score higher in exams. It is important to clear their doubts and boost their confidence. Several students fear maths because they don’t get the concepts right. They solve different concepts that would help them build the ideas. The Important Questions Class 6 Maths Chapter 4 prepared by the experts of Extramarks will help students practise questions from the chapter. There will be other benefits as well. These are-

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• The experts have collected the questions from different sources. They have also included several questions from past years’ question papers. So, students will have ideas about which kind of questions come in exams. They have solved the questions too. Thus, the Chapter 4 Class 6 Maths Important Questions will help students solve questions, boost confidence and score better in exams. 

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