CBSE Important Questions Class 6 Maths Chapter 8 Playing with Constructions

Geometrical construction means drawing accurate shapes using tools such as a ruler, compass and set square. A compass draws circles and arcs because every point on a circle stays at the same distance from its centre.

Accurate construction begins when students stop guessing shapes and start using properties, measurements and tools. CBSE Important Questions Class 6 Maths Chapter 8 helps students practise Playing with Constructions from the 2026 NCERT Ganita Prakash syllabus. The chapter covers compass use, circles, radius, squares, rectangles, rotated figures, diagonals and points equidistant from two given points. These questions support CBSE school exams, notebook construction work, class activities and diagram-based revision. The NCERT chapter also highlights rough diagrams as a useful planning step before construction.

Key Takeaways

• Compass: A compass draws circles and arcs by keeping a fixed distance from a centre point.
• Circle: All points on a circle stay at the same distance from its centre.
• Rectangle: A rectangle has equal opposite sides and all angles equal to 90°.
• Square: A square has all sides equal and all angles equal to 90°.

CBSE Important Questions Class 6 Maths Chapter 8 Structure 2026

Class 6 Maths Chapter 8 Important Questions with Answers

Students must know the meaning of each construction term before drawing figures. These class 6 maths chapter 8 important questions test NCERT definitions, tools and basic reasoning.

1. What is geometrical construction in Class 6 Maths?

Geometrical construction means drawing accurate shapes using tools such as a ruler and compass.

1. A ruler helps draw straight lines.
2. A compass helps draw circles and arcs.
3. A rough diagram helps plan the final figure.

Final Answer: Geometrical construction means drawing accurate figures with proper tools.

2. What can we draw with a compass?

A compass can draw circles and parts of circles called arcs.

1. Keep the metal tip fixed at one point.
2. Keep the pencil at a fixed distance.
3. Move the pencil around the fixed point.

Final Answer: A compass draws circles and arcs.

3. What is the centre of a circle?

The centre of a circle is the fixed point from which all circle points stay equally distant.

1. The compass tip stays at the centre.
2. The pencil moves around it.
3. Every point on the circle has the same distance from it.

Final Answer: The fixed middle point is the centre.

4. What is the radius of a circle?

The radius is the distance from the centre to any point on the circle.

1. The radius stays fixed while drawing a circle.
2. It controls the size of the circle.
3. A larger radius gives a larger circle.

Final Answer: Radius is the centre-to-circle distance.

5. If all points are 4 cm away from point P, what shape do they form?

All points 4 cm away from point P form a circle.

1. Point P becomes the centre.
2. 4 cm becomes the radius.
3. A compass can mark all such points.

Given Data:
Centre = P
Radius = 4 cm

Final Answer: They form a circle with centre P and radius 4 cm.

6. Why does a compass draw a circle accurately?

A compass draws a circle accurately because it keeps the same radius while moving.

1. The compass tip stays fixed.
2. The pencil remains at a fixed distance.
3. This creates points equidistant from the centre.

Final Answer: A compass keeps the radius fixed.

Class 6 Maths Chapter 8 Playing with Constructions Questions

The NCERT chapter uses art, waves and figures to make construction visual. These class 6 maths chapter 8 Playing with Constructions questions connect compass work with real drawing tasks.

7. Why should students draw a rough diagram before construction?

A rough diagram helps students decide the order of construction steps.

1. It shows the final shape roughly.
2. It marks known lengths and angles.
3. It helps identify which point to locate first.

Final Answer: A rough diagram helps plan construction.

8. What is the use of a ruler in constructions class 6 maths?

A ruler helps draw straight line segments and measure given lengths.

1. It marks exact distances.
2. It joins two points neatly.
3. It helps construct sides of squares and rectangles.

Final Answer: A ruler draws and measures straight line segments.

9. What is the use of a compass in constructions class 6 maths?

A compass transfers equal lengths and draws circles or arcs.

1. It can mark points at a fixed distance.
2. It helps avoid trial and error.
3. It supports square, rectangle and house constructions.

Final Answer: A compass draws arcs and transfers equal distances.

10. What does an arc mean in construction?

An arc is a part of a circle.

1. A compass can draw an arc.
2. It uses a fixed centre and radius.
3. Arcs help locate points in constructions.

Final Answer: An arc is a part of a circle.

11. Why are supporting curves used in construction?

Supporting curves help locate required points accurately.

1. They may not appear in the final figure.
2. They guide compass placement.
3. They reduce guessing during construction.

Final Answer: Supporting curves help find exact construction points.

12. How does a compass help in drawing a wave?

A compass draws each wave as a circular arc or half circle.

1. Choose the centre point carefully.
2. Set a fixed radius.
3. Draw the arc smoothly across the line.

Final Answer: A compass creates equal curved parts in a wave.

Compass and Ruler Constructions Class 6 Questions

Many construction tasks require both measuring and equal-distance marking. These compass and ruler constructions class 6 questions focus on step-by-step tool use.

13. How do you draw a circle of radius 5 cm?

Draw a circle of radius 5 cm by setting the compass opening to 5 cm.

1. Mark a centre point O.
2. Open the compass to 5 cm using a ruler.
3. Keep the tip at O and rotate the pencil.

Given Data:
Radius = 5 cm

Final Result: Circle with centre O and radius 5 cm

14. How do you mark points 3 cm away from a point A?

Mark points 3 cm away from A by drawing a circle with centre A and radius 3 cm.

1. Set the compass opening to 3 cm.
2. Place the tip at A.
3. Draw the circle or required arc.

Given Data:
Centre = A
Radius = 3 cm

Final Result: All points on the circle are 3 cm from A

15. Why is compass construction better than trial and error?

Compass construction is better because it marks all points at a fixed distance accurately.

1. Trial and error takes more time.
2. A compass keeps the distance fixed.
3. Intersecting arcs locate points neatly.

Final Answer: Compass construction gives faster and more accurate results.

16. How can we transfer a length using a compass?

Transfer a length by setting the compass to that length and marking it elsewhere.

1. Place the compass tips on the given segment.
2. Keep the opening unchanged.
3. Mark the same length on another line.

Final Answer: A compass can copy a length without measuring again.

17. Why should the compass opening not change during construction?

The compass opening should not change because it represents a fixed length.

1. A changed opening changes the radius.
2. The marked point becomes incorrect.
3. Equal sides may become unequal.

Final Answer: The compass opening must stay fixed for accuracy.

Circle Radius Centre Class 6 Important Questions

A circle is central to many Chapter 8 constructions. These circle radius centre class 6 questions test the main rule that all circle points are equidistant from the centre.

18. If a circle has centre O and radius 6 cm, how far is any point on it from O?

Any point on the circle is 6 cm from O.

1. Radius means distance from centre to circle.
2. Every point on a circle has the same radius.
3. The centre is O.

Given Data:
Radius = 6 cm

Final Answer: 6 cm

19. Can two points on the same circle have different distances from the centre?

No, two points on the same circle cannot have different distances from the centre.

1. Every circle point has equal distance from the centre.
2. This distance is the radius.
3. Different distances would not form the same circle.

Final Answer: All points on one circle have the same distance from the centre.

20. What happens when the radius of a circle increases?

The circle becomes larger when the radius increases.

1. Radius controls the distance from centre to boundary.
2. A larger radius places the circle farther from the centre.
3. The circle covers a bigger region.

Final Answer: A larger radius gives a larger circle.

21. What happens when the compass tip moves during circle construction?

The circle becomes inaccurate when the compass tip moves.

1. The centre changes.
2. The radius may not stay fixed.
3. The curve may not remain a proper circle.

Final Answer: The compass tip must stay fixed at the centre.

22. What is the radius when all marked points are 7 cm from centre C?

The radius is 7 cm.

1. Radius means centre-to-circle distance.
2. The centre is C.
3. Every marked point is 7 cm from C.

Given Data:
Distance from C = 7 cm

Final Answer: Radius = 7 cm

Properties of Rectangle Class 6 and Square Construction Class 6 Questions

Squares and rectangles share right angles but differ in side lengths. These properties of rectangle class 6 and square construction class 6 questions follow the NCERT construction logic.

23. What are the two main properties of a rectangle?

A rectangle has equal opposite sides and all angles equal to 90°.

1. Opposite sides have equal length.
2. Each corner is a right angle.
3. A rectangle has four sides.

Final Answer: Opposite sides equal and all angles 90°.

24. What are the two main properties of a square?

A square has all sides equal and all angles equal to 90°.

1. Every side has the same length.
2. Every angle is a right angle.
3. A square is a special rectangle.

Final Answer: All sides equal and all angles 90°.

25. How do you construct a square of side 6 cm?

Construct a square of side 6 cm by drawing equal sides and right angles.

1. Draw PQ = 6 cm.
2. Draw perpendiculars at P and Q.
3. Mark PS = 6 cm and QR = 6 cm.
4. Join S and R.

Given Data:
Side = 6 cm

Final Result: Square PQRS with side 6 cm

26. How do you construct a rectangle of sides 4 cm and 6 cm?

Construct a rectangle of sides 4 cm and 6 cm using opposite equal sides and right angles.

1. Draw AB = 6 cm.
2. Draw a perpendicular at A.
3. Mark AD = 4 cm.
4. Draw perpendiculars and complete ABCD.

Given Data:
Length = 6 cm
Breadth = 4 cm

Final Result: Rectangle ABCD of size 6 cm × 4 cm

27. Can a four-sided figure have all angles 90° but opposite sides unequal?

No, a four-sided figure with all angles 90° has equal opposite sides.

1. A figure with four right angles behaves like a rectangle.
2. A rectangle has equal opposite sides.
3. Opposite sides cannot remain unequal.

Final Answer: No, it is not possible.

28. Is a rotated square still a square?

Yes, a rotated square is still a square.

1. Rotation does not change side lengths.
2. Rotation does not change angle measures.
3. It still has equal sides and 90° angles.

Final Answer: A rotated square remains a square.

29. Is a rotated rectangle still a rectangle?

Yes, a rotated rectangle is still a rectangle.

1. Its opposite sides remain equal.
2. Its angles remain 90°.
3. Only its position changes.

Final Answer: A rotated rectangle remains a rectangle.

Rectangle Construction Class 6 Step-by-Step Questions

Rectangle construction often begins with one known side. These rectangle construction class 6 questions help students write clear steps in CBSE school exams.

30. Construct a rectangle with sides 2 cm and 10 cm.

Draw a rectangle with length 10 cm and breadth 2 cm using perpendiculars.

1. Draw PQ = 10 cm.
2. Draw perpendiculars at P and Q.
3. Mark PS = 2 cm and QR = 2 cm.
4. Join S and R.

Given Data:
Length = 10 cm
Breadth = 2 cm

Final Result: Rectangle PQRS of size 10 cm × 2 cm

31. Why are perpendicular lines needed while constructing a rectangle?

Perpendicular lines are needed because every rectangle angle is 90°.

1. Each corner of a rectangle is a right angle.
2. A perpendicular creates a 90° angle.
3. This keeps the rectangle accurate.

Final Answer: Perpendiculars help create right angles.

32. Why are opposite sides checked after constructing a rectangle?

Opposite sides are checked to confirm the rectangle property.

1. A rectangle must have equal opposite sides.
2. Measurement verifies the construction.
3. It also detects drawing errors.

Final Answer: Equal opposite sides confirm the rectangle.

33. How do you construct a rectangle divisible into two identical squares?

Construct a rectangle whose length is twice its breadth.

1. Choose any side length for one square.
2. Make the rectangle breadth equal to that side.
3. Make the rectangle length twice that side.

Example:
Breadth = 4 cm
Length = 2 × 4 cm = 8 cm

Final Result: Rectangle 8 cm × 4 cm

34. How do you construct a rectangle divisible into three identical squares?

Construct a rectangle whose length is three times its breadth.

1. Choose the side of one square.
2. Take the breadth equal to that side.
3. Take the length three times that side.

Example:
Breadth = 3 cm
Length = 3 × 3 cm = 9 cm

Final Result: Rectangle 9 cm × 3 cm

35. Can a rectangle of sides 7 cm and 2 cm divide into three identical squares?

No, a 7 cm × 2 cm rectangle cannot divide into three identical squares.

1. Three identical squares need length = 3 × breadth.
2. Here, 3 × 2 cm = 6 cm.
3. The actual length is 7 cm.

Final Answer: No, 7 cm is not three times 2 cm.

Diagonals of Rectangle Class 6 and Diagonals of Square Class 6 Questions

A diagonal joins two opposite corners of a rectangle or square. These diagonals of rectangle class 6 and diagonals of square class 6 questions come from the NCERT exploration section.

36. What is a diagonal of a rectangle?

A diagonal of a rectangle is a line segment joining two opposite corners.

1. It connects non-adjacent vertices.
2. A rectangle has two diagonals.
3. The diagonals are usually drawn inside the rectangle.

Final Answer: A diagonal joins opposite corners.

37. How many diagonals does a rectangle have?

A rectangle has two diagonals.

1. One diagonal joins the first pair of opposite corners.
2. The other diagonal joins the second pair.
3. Both lie inside the rectangle.

Final Answer: A rectangle has two diagonals.

38. Are the diagonals of a rectangle equal?

Yes, the diagonals of a rectangle are equal in length.

1. Construct a rectangle.
2. Join both pairs of opposite corners.
3. Measure both diagonals to compare them.

Final Answer: The diagonals of a rectangle are equal.

39. What happens when a rectangle has all four sides equal?

The rectangle becomes a square when all four sides are equal.

1. A rectangle already has four right angles.
2. Equal sides add the square property.
3. It satisfies both square properties.

Final Answer: A rectangle with all sides equal is a square.

40. When does a diagonal divide rectangle angles into equal parts?

A diagonal divides rectangle angles equally when the rectangle is a square.

1. A square has equal sides.
2. Its diagonal divides opposite right angles equally.
3. Each divided angle becomes 45°.

Calculation:
90° ÷ 2 = 45°

Final Answer: This happens in a square.

41. What do you observe when a diagonal divides angles into 45° and 45°?

The rectangle has equal adjacent sides and becomes a square.

1. Each right angle divides equally.
2. Each part measures 45°.
3. Equal division indicates square-like symmetry.

Final Answer: The rectangle is a square.

Rectangle with Diagonal Construction Class 6 Questions

Some constructions give one side and one diagonal instead of both sides. These rectangle with diagonal construction class 6 questions test compass and perpendicular skills.

42. How do you construct a rectangle with one side 5 cm and diagonal 7 cm?

Construct it by drawing one side, a perpendicular line and an arc of radius 7 cm.

1. Draw CD = 5 cm.
2. Draw a perpendicular at C.
3. With D as centre, draw an arc of radius 7 cm.
4. Mark the intersection as B.
5. Complete rectangle ABCD.

Given Data:
Side = 5 cm
Diagonal = 7 cm

Final Result: Rectangle with side 5 cm and diagonal 7 cm

43. Why is an arc used in rectangle construction with a diagonal?

An arc is used to locate a point at the given diagonal distance.

1. The diagonal length fixes the distance.
2. A compass marks all points at that distance.
3. The required corner lies where the arc meets the perpendicular.

Final Answer: The arc helps locate the missing vertex.

44. Construct a rectangle with one side 4 cm and diagonal 8 cm.

Draw a 4 cm side and use an 8 cm arc from the opposite endpoint.

1. Draw CD = 4 cm.
2. Draw a perpendicular at C.
3. Draw an arc of radius 8 cm from D.
4. Mark the intersection as B.
5. Complete the rectangle.

Given Data:
Side = 4 cm
Diagonal = 8 cm

Final Result: Rectangle with side 4 cm and diagonal 8 cm

45. Construct a rectangle with one side 3 cm and diagonal 7 cm.

Draw a 3 cm side and locate the opposite corner using a 7 cm arc.

1. Draw CD = 3 cm.
2. Draw a perpendicular at C.
3. Draw an arc of radius 7 cm from D.
4. Mark the meeting point as B.
5. Complete rectangle ABCD.

Given Data:
Side = 3 cm
Diagonal = 7 cm

Final Result: Rectangle with side 3 cm and diagonal 7 cm

Points Equidistant from Two Points Class 6 Questions

A point equidistant from two given points lies at the same distance from both. The NCERT house construction uses this idea to locate the top point through intersecting arcs.

46. What does equidistant from two points mean?

Equidistant from two points means having the same distance from both points.

1. The point must satisfy two distance conditions.
2. A compass can mark equal distances.
3. Intersecting arcs can locate such a point.

Final Answer: Equidistant means equally far from both points.

47. How do you locate a point 5 cm from both B and C?

Locate it by drawing two arcs of radius 5 cm from B and C.

1. Set compass radius to 5 cm.
2. Draw an arc from B.
3. Draw another arc from C.
4. Mark the intersection point.

Given Data:
Distance from B = 5 cm
Distance from C = 5 cm

Final Result: The arc intersection gives the required point

48. Why do two arcs help in locating an equidistant point?

Two arcs help because their intersection satisfies both distance conditions.

1. One arc shows points at fixed distance from B.
2. The other arc shows points at fixed distance from C.
3. Their intersection is at the required distance from both.

Final Answer: The intersection point is equidistant from both centres.

49. How can you construct a house shape with all border lines of 5 cm?

Construct the base and use equal-radius arcs to locate the top point.

1. Draw the lower parts using 5 cm sides.
2. Draw arcs of radius 5 cm from the two upper corner points.
3. Mark the arc intersection as the roof point.
4. Join the roof point to both upper corners.

Given Data:
Each border line = 5 cm

Final Result: House figure with equal 5 cm border lines

50. Is it necessary to draw full circles to locate the roof point?

No, only arcs near the required point are enough.

1. Full circles take more space.
2. Arcs show the needed intersection.
3. The compass radius remains the same.

Final Answer: Arcs are enough for locating the point.

51. Can a four-sided figure have all sides equal but not be a square?

Yes, a four-sided figure can have all sides equal but not be a square.

1. A square needs equal sides and four right angles.
2. A rhombus has all sides equal.
3. A rhombus need not have 90° angles.

Final Answer: Yes, a rhombus is such a figure.

Class 6 Maths Chapter 8 Extra Questions for CBSE Practice

These class 6 maths chapter 8 extra questions cover quick recall, construction reasoning and exam-style statements. Students should draw figures wherever a construction answer needs proof.

52. Fill in the blank: A compass is used to draw ______.

A compass is used to draw circles and arcs.

1. It keeps a fixed radius.
2. It rotates around a centre.
3. It creates curved shapes accurately.

Final Answer: Circles and arcs.

53. Fill in the blank: All angles of a rectangle measure ______.

All angles of a rectangle measure 90°.

1. A rectangle has four angles.
2. Each angle is a right angle.
3. This property helps in construction.

Final Answer: 90°.

54. Fill in the blank: All sides of a square are ______.

All sides of a square are equal.

1. A square has four sides.
2. Each side has the same length.
3. It also has four right angles.

Final Answer: Equal.

55. True or False: A square remains a square after rotation.

True, a square remains a square after rotation.

1. Its side lengths do not change.
2. Its angle measures do not change.
3. Only its position changes.

Final Answer: True.

56. True or False: A rectangle has only one diagonal.

False, a rectangle has two diagonals.

1. Each diagonal joins opposite corners.
2. There are two pairs of opposite corners.
3. Therefore, two diagonals are possible.

Final Answer: False.

57. True or False: Supporting lines may help even if they are not part of the final figure.

True, supporting lines may help in construction.

1. They guide point placement.
2. They support accurate drawing.
3. They can remain light or be erased later.

Final Answer: True.

58. Choose the correct option: Which tool helps transfer equal lengths?

1. Compass
   b. Eraser
   c. Protractor only
   d. Notebook margin

A compass helps transfer equal lengths.

1. It can hold a fixed opening.
2. The same opening marks equal distances.
3. It also draws arcs.

Final Answer: a. Compass.

59. Choose the correct option: Which figure has all sides equal and all angles 90°?

1. Rectangle
   b. Square
   c. Circle
   d. Arc

A square has all sides equal and all angles 90°.

1. A rectangle has equal opposite sides.
2. A square has all four sides equal.
3. Both have right angles.

Final Answer: b. Square.

60. Choose the correct option: Which construction tool draws a straight line segment?

1. Compass
   b. Ruler
   c. Divider only
   d. Thread

A ruler draws a straight line segment.

1. It has a straight edge.
2. It can measure length.
3. It joins two points neatly.

Final Answer: b. Ruler.

Important Questions Class 6 Maths