Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 8: Play with Constructions

Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics  Chapter 8: Play with Constructions

Section A — Multiple Choice Questions

1. The instrument used to draw a circle is:
   a) Ruler b) Compass c) Divider d) Protractor (Identifies and uses construction instruments)

2. The angle on a straight line is:
   a) 45° b) 60° c) 90° d) 180°
   (Understands basic angle measures)

3. To bisect a line segment we use:
   a) Ruler only b) Compass only c) Ruler and compass d) Divider only (Performs basic constructions)

4. A perpendicular bisector divides a line segment into:
   a) 3 equal parts b) 2 equal parts at 90° c) 2 unequal parts d) Parallel parts (Perpendicular bisector concept)

5. Two lines that never meet and remain at a constant distance are called:
   a) Intersecting b) Perpendicular c) Skew d) Parallel (Parallel lines)

6. Which set of lengths cannot form a triangle?
   a) 3 cm, 4 cm, 5 cm b) 2 cm, 3 cm, 6 cm c) 4 cm, 6 cm, 7 cm d) 5 cm, 5 cm, 8 cm
   (Triangle inequality)

7. The diagonals of a rhombus:
   a) Do not bisect each other b) Bisect each other at right angles c) Are equal but not perpendicular d) Are parallel (Rhombus properties)

8. To draw a 120° angle using constructions, you first construct:
   a) 30° b) 45° c) 60° d) 90° (Angle construction)

9. Stepping the radius around a circle produces a regular:
   a) Pentagon b) Hexagon c) Octagon d) Square (Regular polygon from circle)

10. The instrument used to transfer a distance from one place to another is:
    a) Compass b) Divider c) Protractor d) Ruler (Using divider)

11. In constructing an equilateral triangle on base AB, the number of arcs drawn with radius AB is:
    a) 1 b) 2 c) 3 d) 4 (Construction process for equilateral triangle)

12. To draw a line perpendicular to a given line at a point on it, we need:
    a) Protractor only b) Compass and ruler c) Divider only d) Set-square only (Perpendicular construction)

13. A square has:
    a) 4 equal sides and 4 right angles b) 4 equal sides, angles unequal c) Only 2 equal sides d) No equal sides (Properties of square)

14. Which angle is not easily constructible with straightedge & compass bisections/additions?
    a) 30° b) 45° c) 75° d) 77° (Feasible angles by construction)

15. To bisect an angle ∠ABC, arcs are drawn:
    a) From both arms BA and BC b) From one arm only c) From the vertex B only d) From midpoint of AB (Angle bisector method)

16. In an equilateral triangle, each interior angle equals:
    a) 45° b) 60° c) 90° d) 120° (Triangle angle facts)

17. A quadrilateral that can be constructed from perpendicular diagonals that bisect each other is a:
    a) Square b) Rectangle c) Rhombus d) Kite only (Quadrilateral from diagonals)

18. From a circle, which of the following can be constructed by stepping equal chords?
    a) Triangle b) Square c) Hexagon d) All of these (Constructions from a circle)

19. A 5 cm segment is bisected. Each part equals:
    a) 5 cm b) 2.5 cm c) 2 cm d) 1.5 cm (Measurement understanding)

20. To construct a triangle with sides 4 cm, 5 cm, 6 cm, which rule must hold?
    a) Pythagoras Theorem b) Triangle inequality c) Parallel postulate d) Exterior angle property (Pre-check for triangle construction)
    Section B — Assertion & Reasoning

Options for each: 

(a) Both A and R true, R explains A; 

(b) Both true, R not explanation; 

(c) A true, R false; 

(d) A false, R true.

1. A: A square can be constructed using a compass and ruler.
   R: All angles of a square are right angles. (Square construction)

2. A: The diagonals of a rhombus bisect each other at right angles.
   R: A rhombus has four equal sides. (Rhombus properties)

3. A: A triangle with sides 2 cm, 3 cm, 6 cm is possible.
   R: The sum of any two sides must be greater than the third side.
   (Triangle inequality)
   A: To draw 30°, a protractor is essential.
   R: A 60° angle can be constructed and then bisected to get 30°. (Angle construction)
   A: The diagonals of a rectangle are equal.
   R: All sides of a rectangle are equal. (Rectangle properties)

4. A: A perpendicular bisector divides a line into two equal parts at 90°.
   R: Perpendicular bisectors help locate midpoints. (Perpendicular bisector)

5. A: A regular hexagon can be drawn inside a circle.
   R: Six equal chords can be marked around the circle using the radius. (Regular polygon from circle)

6. A: Every equilateral triangle is isosceles.
   R: An isosceles triangle has at least two equal sides. (Triangle classification)

7. A: Parallel to a given line through a point can be drawn using only compass and ruler.
   R: A protractor is necessary to draw parallel lines. (Parallel line construction)

8. A: The diagonals of a square are unequal.
   R: A square has four equal sides. (Square properties)

9. A: A rhombus has four right angles.
   R: Its diagonals are perpendicular to each other. (Rhombus vs square)

10. A: A circle can be drawn without a compass.
    R: A compass is the standard instrument to draw circles. (Instruments)

11. A: A trapezium has exactly one pair of parallel sides.
    R: A parallelogram also has exactly one pair of parallel sides. (Quadrilateral classification)

12. A: A triangle with angles 90°, 60°, and 30° is possible.
    R: The sum of angles in a triangle is 180°. (Angle sum property)

13. A: Every rectangle is a parallelogram.
    R: Opposite sides of a rectangle are parallel and equal. (Relationship among quadrilaterals)

14. A: A regular hexagon is constructible by compass.
    R: It is obtained by marking six equal arcs on a circle. (Regular polygon construction)

15. A: An angle bisector divides the angle into three equal parts.
    R: A bisector divides an angle into two equal parts. (Angle bisector concept)

16. A: A set-square can be used to draw perpendicular lines.
    R: A 45°–45°–90° set-square has a right angle. (Instruments)

17. A: A divider measures angles.
    R: A divider transfers distances accurately. (Instruments—divider)

18. A: A circle has only one diameter.
    R: A circle has infinitely many diameters. (Circle properties)

Section C — True/False

1. A compass can be used to measure an angle. (Instrument usage)

2. A perpendicular bisector divides a line segment into two equal parts at 90°. (Perpendicular bisector)

3. A regular hexagon can be constructed using a compass. (Regular polygon construction)

4. If the sum of any two sides equals the third side, a triangle is not possible. (Triangle inequality)

5. The diagonals of a rhombus are always equal. (Rhombus vs square)

6. Every square is a rectangle. (Quadrilateral hierarchy)

7. 45° is not constructible by compass and ruler. (Angle construction)

8. A line parallel to a given line can be drawn using compass and ruler. (Parallel construction)

9. The circumcentre of an acute triangle lies inside the triangle. (Triangle centres—informal)

10. A divider is used to transfer lengths. (Divider usage)

Section D — Short Answer I (2 Marks each)

1. Construct a perpendicular bisector of a 7 cm line segment. (Perpendicular bisector) 

2. Construct an angle of 60° using only compass and ruler. [Insert NCERT Figure Placeholder here] (Angle construction)

3. Construct an angle of 30° using bisection. (Angle bisection)

4. Draw an equilateral triangle of side 5 cm. (Equilateral construction)

5. Draw a perpendicular to a line at a given point on it. (Perpendicular from on-line point)

6. Draw a perpendicular to a line from a point outside it. (Perpendicular from external point)

7. Construct an angle of 90°. (Right-angle construction)

8. Bisect an acute angle ∠XYZ. (Angle bisector)

9. Draw a line parallel to a given line through a point not on it (equal angle/copy angle method). (Parallel line construction)

10. Construct a triangle with sides 4 cm, 5 cm, 6 cm (SSS). (Triangle by SSS)

11. Construct an angle of 120°. (Compound angle construction)

12. Construct a square of side 4 cm. (Square construction)

13. Construct a rectangle with sides 6 cm and 4 cm. (Rectangle construction)

14. Divide a 9 cm line segment into 3 equal parts by compass. (Division of a segment)

15. Construct an equilateral triangle inscribed in a given circle. (Inscribed figures)

Section E — Short Answer II (3 Marks each)

1. Construct the perpendicular bisector of a 6 cm line segment and verify it. (Construction + verification)
   Draw a line parallel to a given line through a point outside it; justify why they are parallel. (Parallel via equal corresponding angles)

2. Construct an equilateral triangle inside a circle of radius 3 cm; explain why it is equilateral. (Equal chords)

3. Construct an isosceles triangle with base 5 cm and equal sides 6 cm; state which angles are equal. (SSS with equal sides)

4. Construct a 90° angle and then bisect it; name the resulting angle. (Angle bisection)
   Construct a rhombus given its diagonals 7 cm and 9 cm; justify equal sides. (Rhombus from diagonals)

5. Construct a square inscribed in a circle of radius 4 cm; explain why angles are right angles. (Diameter and central angle)

6. Draw a trapezium with one pair of parallel sides 7 cm and 5 cm; indicate the parallel sides. (One-pair-parallel quadrilateral)

7. Construct an equilateral triangle of side 4.5 cm and explain why each angle is 60°. (Equilateral properties)

8. Construct a regular hexagon in a circle of radius 2.5 cm; explain chord–radius equality. (Regular hexagon from equal chords)

Section F — Long Answer (5 Marks each)

1. Construct a rhombus with diagonals 6 cm and 8 cm; write steps and prove all sides are equal. (Rhombus via diagonals) 

2. Construct a triangle with sides 5 cm, 6 cm, 7 cm (SSS); justify the construction. (SSS triangle)
   Construct a square of side 6 cm; verify that diagonals are equal and perpendicular bisectors. (Square properties)

3. Construct a rectangle 7 cm × 4 cm; show opposite sides are equal and parallel. (Rectangle properties)

4. Construct an equilateral triangle of side 6 cm; explain why each angle is 60°. (Equilateral triangle)

5. Construct an angle of 75° using only compass and ruler; explain the method used. (Angle composition)  

6. Construct an angle of 135°; describe two different ways to obtain it. (Angle addition/subtraction)

7. Construct a parallelogram with sides 6 cm and 5 cm and included angle 60°; explain why opposite sides are parallel.  (Parallelogram construction)

8. Construct a square inscribed in a circle of radius 3 cm; justify that its diagonals are diameters. (Inscribed square)

9. Construct an isosceles triangle with base 5 cm and equal sides 7 cm; prove base angles are equal.  (Isosceles triangle theorem—construction)

Section G — Case-Based Questions (CBQ)

Case 1 – Triangular Park (Equilateral layout)

A group of students is asked to design a small triangular park for their school exhibition. The boundary of the park must be drawn as an equilateral triangle of side 4 cm in the plan drawing. They are required to use ruler and compass to prepare the figure and then answer questions about its angles and perimeter.

Q1. The type of triangle is: a) Scalene b) Isosceles c) Equilateral d) Right (Identifying figure)
Q2. The most suitable tool to construct the triangle is: a) Protractor b) Compass c) Set-square d) Divider (Instrument selection)
Q3. Sum of interior angles = ___: a) 90° b) 120° c) 180° d) 360° (Angle-sum)
Q4. Perimeter on plan = ___ cm: a) 8 b) 10 c) 12 d) 16 (Perimeter)

Case 2 – Kite Frame (Rhombus diagonals)

During the school craft fair, students prepare a kite frame using thin sticks. The kite is to be in the shape of a rhombus where the two diagonals are 8 cm and 6 cm. To draw the plan of this kite, the diagonals are first constructed and then joined to get the rhombus. The students also discuss the properties of the rhombus based on its diagonals and sides.

Q1. The property of diagonals used is: a) Equal b) Perpendicular and bisecting c) Parallel d) Unequal (Rhombus property)
Q2. The figure constructed is: a) Rectangle b) Rhombus c) Square d) Trapezium (Identify by diagonals)
Q3. Instruments needed mainly: a) Protractor b) Compass + Ruler c) Set-square only d) Divider only (Instrument use)
Q4. All sides of the rhombus are: a) Equal b) Unequal c) Two equal d) Opposite equal (Rhombus sides)

Case 3 – Playground Plan (Rectangle)

The sports teacher wants a rectangular playground in the scaled drawing of the school. The length is 20 m and breadth is 15 m. Students are asked to calculate the perimeter and area of the playground and also highlight the geometrical properties of a rectangle.

Q1. Adjacent sides meet at: a) 30° b) 60° c) 90° d) 120° (Right angle)
Q2. Perimeter = ___ m: a) 50 b) 60 c) 70 d) 80 (Perimeter)
Q3. Area = ___ m²: a) 200 b) 250 c) 300 d) 350 (Area)
Q4. Opposite sides are: a) Unequal b) Equal and parallel c) Equal only d) Parallel only (Rectangle properties)

Case 4 – Hexagon Tiles (Regular hexagon in a circle)

A classroom activity involves designing floor tiles in the shape of regular hexagons, each having side 5 cm. To construct them, students are asked to draw a circle and step off equal chords using a compass. They then calculate the perimeter of one tile and discuss the angle properties of a regular hexagon.

Q1. Number of sides = a) 4 b) 5 c) 6 d) 8 (Polygon)
Q2. Interior angle of regular hexagon = a) 90° b) 108° c) 120° d) 135° (Polygon angles—informal)
Q3. Perimeter of one tile = a) 20 cm b) 25 cm c) 30 cm d) 36 cm (Perimeter)
Q4. Tool to step equal chords on circle: a) Protractor b) Compass c) Ruler d) Set-square (Instrument use)

Case 5 – Clock Hands (Right angle and bisection)

Ravi looks at the clock when the time is exactly 3 o’clock. He notices that the two hands of the clock are at a right angle (90°). His teacher then asks the class to construct a right angle using compass and ruler, measure it with a protractor, and also explore how any angle can be bisected.

Q1. The angle between hands is: a) 30° b) 60° c) 90° d) 120° (Angle sense)
Q2. To construct a right angle, we use: a) Compass method b) Divider c) Only ruler d) None (Right-angle construction)
Q3. Instrument to measure the angle: a) Protractor b) Compass c) Divider d) Ruler (Measurement)
Q4. Any angle can be bisected using: a) Protractor b) Ruler only c) Compass + Ruler d) Set-square only (Angle bisection)

Image NCERT Textbook Figure 

Hexagon in Circle(Page 188–189)]

•  NCERT Textbook Figure — Perpendicular from a Point (Page 195–196) ]
  NCERT Textbook Figure — Square/Rectangle Construction (Page 195–197)] 

•  NCERT Textbook Figure — Angle Bisector (Page 205–207)]
  NCERT Textbook Figure — 60°, 30°, 90°, 120° Constructions (Page 205–207)]
                     

•  NCERT Textbook Figure — SSS Triangle(Page 211–214) ] NCERT Textbook Figure — Perpendicular Bisector (Page 211–213)] ]
       

 NCERT Textbook Figure — Rhombus by Diagonals (Page 215–216)]