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About Playing with Constructions — Class 6 CBSE

Construct line segments, circles, and angles using ruler and compass. This topic is part of the CBSE Class 6 mathematics syllabus (chapter: Chapter 8). On this page you can practice 59 questions across three difficulty levels — 20 easy, 20 medium, and 19 hard — each with a visual step-by-step solution, plus a timed 34-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Playing with Constructions

  • Introduction to Geometric Constructions and Tools
  • Constructing Line Segments of Specific Lengths
  • Constructing Circles with a Compass
  • Constructing a Perpendicular Bisector of a Line Segment
  • Copying a Line Segment and Preparing for Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Playing with Constructions — solved examples for Class 6 CBSE

Example 1easy

Which instrument from your geometry box is primarily used to draw a circle of a given radius?
  1. A)A) Ruler
  2. B)B) Protractor
  3. C)C) Compass
  4. D)D) Set-square

Step-by-step solution

  1. A ruler is used for drawing straight lines and measuring lengths.
  2. A protractor is used for measuring and drawing angles.
  3. A compass has two arms, one with a pencil and one with a pointed tip. The pointed tip is fixed at the center, and the pencil arm rotates to draw a circle, keeping the radius constant.
  4. Set-squares are used for drawing parallel and perpendicular lines.

Answer: C) Compass

Example 2medium

Which tool from a geometry box is primarily used to draw circles and arcs?
  1. A)Ruler
  2. B)Protractor
  3. C)Compass
  4. D)Divider

Step-by-step solution

  1. The compass has two arms, one with a pencil and the other with a pointer. It is specifically designed for drawing circles and arcs by fixing the radius and rotating one arm around a fixed point (the centre).

Answer: Compass

Example 3hard

When constructing the perpendicular bisector of a line segment, which tool is *most crucial* for ensuring that the two arcs drawn from the endpoints have exactly the same radius and thus intersect at points equidistant from the endpoints?
  1. A)Ruler
  2. B)Protractor
  3. C)Divider
  4. D)Compass

Step-by-step solution

  1. The compass is the only tool among the given options that can draw arcs and maintain a fixed radius accurately.
  2. When constructing a perpendicular bisector, the compass is used to draw arcs of the same radius from both endpoints of the line segment.
  3. This ensures that the intersection points of these arcs are equidistant from the endpoints, which is fundamental to the perpendicular bisector construction.

Answer: Compass

Practice questions on Playing with Constructions

  1. Q1.easy

    To draw a line segment AB of length 5.5 cm using a ruler, where should you place the pencil's starting point on the ruler to mark 'A' accurately?
    1. A)A) At the 0 cm mark
    2. B)B) At the 1 cm mark
    3. C)C) At any random mark
    4. D)D) At the 5.5 cm mark
    Show answer

    Answer: A) At the 0 cm mark

    Hint: For precise measurements, always begin your measurement from the standard starting point on any measuring instrument.

  2. Q2.easy

    When copying a line segment PQ using a compass and ruler, which of the following is the correct first step after drawing a ray?
    1. A)A) Draw another line segment of any length.
    2. B)B) Open the compass to the length of PQ.
    3. C)C) Measure PQ with a ruler and then draw.
    4. D)D) Mark a point on the ray and draw an arc of any radius.
    Show answer

    Answer: B) Open the compass to the length of PQ.

    Hint: The goal is to transfer the exact length of the given line segment. How do you capture that length accurately with a compass?

  3. Q3.easy

    A circle is a closed curve where every point on the curve is _______________ from a fixed central point.
    1. A)A) at a different distance
    2. B)B) equidistant
    3. C)C) twice the distance
    4. D)D) half the distance
    Show answer

    Answer: B) equidistant

    Hint: Think about the definition of a circle and what the radius represents in relation to the center and the curve.

  4. Q4.medium

    To draw a line segment of length 7.5 cm using a ruler, what is the correct procedure?
    1. A)Mark a point A, then mark a point B at 7.5 cm from A, and join A to B.
    2. B)Mark a point A, then open the compass to 7.5 cm and draw an arc.
    3. C)Draw a random line and measure 7.5 cm on it.
    4. D)Draw two points 7 cm apart.
    Show answer

    Answer: Mark a point A, then mark a point B at 7.5 cm from A, and join A to B.

    Hint: A ruler is used to measure and draw straight lines of specific lengths.

  5. Q5.medium

    What two pieces of information are essential and sufficient to construct a unique circle using a compass?
    1. A)Length of its diameter and one point on its circumference.
    2. B)Its centre and the length of its radius.
    3. C)Length of its chord and its centre.
    4. D)Three points on its circumference.
    Show answer

    Answer: Its centre and the length of its radius.

    Hint: Think about how you set up a compass to draw a circle. What do you fix first?

  6. Q6.medium

    Which of the following statements is TRUE about the perpendicular bisector of a line segment?
    1. A)It divides the line segment into two unequal parts.
    2. B)It forms an acute angle with the line segment.
    3. C)Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.
    4. D)It passes through only one endpoint of the line segment.
    Show answer

    Answer: Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.

    Hint: Remember what 'bisector' and 'perpendicular' mean in this context.

  7. Q7.hard

    Two friends, Ananya and Rohan, live at points A and B respectively. They want to find a location for a new park 'P' such that it is exactly equidistant from both their houses. Which geometric construction should they use to find the *locus* of all possible points for the park P?
    1. A)Angle bisector of ∠APB
    2. B)Perpendicular bisector of line segment AB
    3. C)Line segment joining A and B
    4. D)A circle with center A and radius AB
    Show answer

    Answer: Perpendicular bisector of line segment AB

    Hint: Consider the definition of a perpendicular bisector and its property regarding points equidistant from the endpoints of the segment.

  8. Q8.hard

    When constructing the bisector of an angle ∠XYZ, after drawing an arc from vertex Y to cut arms YX and YZ at points M and N respectively, why is it essential to draw two more arcs of the *same radius* from M and N to intersect each other?
    1. A)To ensure the bisector is perpendicular to the angle arms.
    2. B)To make the angle bisector longer.
    3. C)To locate a point that is equidistant from the arms YX and YZ.
    4. D)To check if the angle is acute or obtuse.
    Show answer

    Answer: To locate a point that is equidistant from the arms YX and YZ.

    Hint: Recall the fundamental property of an angle bisector regarding distances from its points to the arms of the angle.

  9. Q9.hard

    Using only a ruler and compass, which of the following angles requires at least *two distinct angle bisection steps* after initially constructing a 60° angle?
    1. A)90°
    2. B)120°
    3. C)30°
    4. D)15°
    Show answer

    Answer: 15°

    Hint: Think about how each angle can be derived from a 60° angle using bisection. How many times do you need to halve an angle to get to the target angle?

These are 9 of the 59 questions available for Playing with Constructions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.