CBSE Important Questions for Class 6 Maths Playing with Constructions - 2025-26
1. Name the main tools used for constructions in geometry.
Ans: The main tools are a ruler, compass, and protractor.
2. What is the purpose of constructing a perpendicular bisector?
Ans: It divides a line segment into two equal parts at a 90° angle.
3. How do you construct a line segment of 5 cm?
Ans: Use a ruler to measure and draw a straight line exactly 5 cm long.
4. What does "constructing an angle" involve?
Ans: Constructing an angle involves drawing an angle of a specific measure using tools like a compass and a protractor.
5. What is an equilateral triangle?
Ans: An equilateral triangle is a triangle with all three sides of equal length and all angles equal to 60°.
6. Describe the steps to construct a 90° angle using a compass and ruler.
Ans: Draw a straight line and mark a point on it. Place the compass on this point and draw an arc that crosses the line. From where the arc crosses the line, draw two more arcs that intersect above the line. Connect the intersection to the point on the line to create a 90° angle.
7. How would you construct a 45° angle?
Ans: Start by constructing a 90° angle as explained. Then, using a compass, divide the 90° angle in half to get a 45° angle.
8. Explain how to draw a line segment that is the perpendicular bisector of another line segment.
Ans: Draw a line segment and mark its endpoints. Place the compass on one endpoint, with a width slightly more than half the segment's length. Draw arcs above and below the line. Repeat from the other endpoint. Connect the intersections of the arcs above and below the line to form a perpendicular bisector.
9. What are the steps to construct a triangle with sides of 4 cm, 5 cm, and 6 cm?
Ans: Draw the base of 6 cm with a ruler. Place the compass at one end, adjust it to 4 cm, and draw an arc. Repeat with 5 cm from the other end. The point where the arcs intersect forms the third vertex of the triangle. Connect this point to each end of the base.
10. Why is constructing angles and shapes important in geometry?
Ans: Constructing angles and shapes accurately is essential for understanding geometry principles and helps in real-life applications like design, building, and art.
11. Construct a circle of diameter 5 cm.
Ans:
Steps of construction:
(i) Draw a line segment AB measuring 5 cm.
(ii) Use a ruler to locate and mark the midpoint O of line segment AB.
(iii) With OO as the centre and the compass opened to the length of OA or OB, draw a circle.
Thus, it is a required circle.
12. Construct a rectangle having adjacent sides of 6 cm and 4 cm and find its area.
Ans:
Given: Adjacent sides are 6 cm and 4 cm.
Steps for construction:
Start by sketching a rough diagram and marking the given measurements.
Draw a line segment AB of 6 cm.
At point A, use a protractor to draw a line AX perpendicular to AB.
With A as the centre, draw an arc with a radius of 4 cm to intersect AX at point D.
Now, with DD as the centre, draw an arc of a 6 cm radius above the line segment AB.
Using B as the centre, draw another arc with a 4 cm radius to intersect the previous arc at point C. Connect B to C and C to D.
This completes the rectangle ABCD.
Area of Rectangle= length×breadth = 6cm×4cm = 24sq cm.
Solve Some Extra Questions for More Practise
1. Identify if there are any squares in this collection. Use measurements if needed.
Think: Is it possible to reason out if the sides are equal or not, and if the angles are right or not without using any measuring instruments in the above figure? Can we do this by only looking at the position of corners in the dot grid?
Ans:
Fig. I: In this figure, AB and BC are not equal. So, ABCD cannot be a square.
Fig. II: In this figure, ∠BAD is not equal to 90°. So, ABCD cannot be a square.
Fig. III: In this figure, counting dots between sides, we find that AB, BC, CD, and DA are all equal sides. Also, the position of the dots on the sides shows, that each angle of ABCD is 90°.
∴ ABCD is a square.
Fig. IV: In this figure, counting dots between sides, we find that AB, BC, CD, and DA are all equal sides. Also, using a protractor, we find that each angle of ABCD is 90°.
∴ ABCD is a square.
2. Is it possible to construct a 4-sided figure in which—
• all the angles are equal to 90º but
• opposite sides are not equal?
Ans: Step 1. Using a ruler, draw a line AB equal to 6 cm, say. (Fig. 1).
Step 2. Using a protractor, draw perpendicular lines at A and B (Fig. 2).
Step 3. Using a ruler, mark point P on the perpendicular at A such that AP = 4 cm.
Using a ruler, mark point Q on the perpendicular at B such that BQ = 2 cm, which is not equal to AP. (Fig. 3).
Step 4. In Fig. 3, the opposite sides of AP and BQ are not equal. Join P and Q using a ruler. Erase the lines above P and Q (Fig. 4).
Step 5. Using a protractor, we find that neither ∠P nor ∠Q is 90°.
Step 6. We conclude that it is not possible to construct a 4-sided figure in which all angles are 90° and opposite sides are not equal.
3. Try to recreate ‘A Person’, ‘Wavy Wave’, and ‘Eyes’ from the section ‘Artworkʼ, using ideas involved in the ‘House’ construction.
Ans: A Person
Wavy Wave
Eyes
4. Take a central line of a different length and try to draw the wave on it.
Ans: Step 1. We start with the central line of different lengths, say, 10 cm. (Figure 1)
Step 2. Since
10 ÷ 2 = 5, using a ruler, take point C on AB such that AC = 5 cm. C is the mid-point of AB.
As 5 ÷ 2 = 2.5, using a ruler, take points D on AC and E on CB such that AD = 2.5 cm and CE = 2.5 cm.
D is the mid-point of AC and E is the mid-point of CB. (Figure 2)
Step 3. With the centre at D, draw a half circle above the central line AB and of radius 2.5 cm. With the centre at E, draw a half circle below the central line AB and of radius 2.5 cm. (Figure 3)
Step 4. Draw vertical lines in the half circles above and below the line AB. (Figure 4)
Step 5. The figure represents the required depiction of the given “Wavy Wave” with the central line of length 10 cm.
5. What radius should be taken in the compass to get this half circle? What should be the length of AX?
Ans: We have AB = 8 cm.
Since the “Wavy Wave” has two equal half circles, we have AX = XB.
∴ X is the mid-point of AB.
∴ AX = $\frac{8}{2}= 4 cm$
∴ The length of AX is 4 cm.
Let M be the mid-point of AX.
∴ AM = MX = $\frac{8}{2}= 4 cm$
The centre of the half circle is M.
∴ Radius of half circle = AM = 2 cm
∴ The radius of the half circle is 2 cm.
This page is all about CBSE Class 6 Maths Important Questions for Chapter 8 – Playing With Constructions. Vedantu makes learning simple with expert-created questions to provide extra practice and help you score better on your test papers.
Here, you will also find short question answers to strengthen your understanding and improve your confidence in construction.
Related Study Materials for Class 6 Maths Chapter 8 Playing with Constructions
CBSE Class 6 Maths Chapter-wise Important Questions
Important Related Links for CBSE Class 6 Maths
FAQs on CBSE Important Questions for Class 6 Maths Playing with Constructions - 2025-26
1. What are the most important types of questions to practice from Chapter 8, Playing with Constructions, for the 2025-26 exam?
For the 2025-26 exams, students should focus on questions that require practical skills. The most frequently asked types include:
- Constructing a perpendicular bisector of a given line segment.
- Constructing an angle of a specific measure (like 60°, 90°, 45°, 120°) using only a ruler and compass.
- Constructing the bisector of a given angle.
- Drawing a circle of a given radius and marking its parts (centre, radius, diameter).
2. How are marks awarded for construction questions in the Class 6 Maths exam?
Marks for construction questions are typically divided to assess different skills. To score full marks, you must ensure:
- Accuracy: The final drawing must be precise, with correct lengths and angles.
- Construction Arcs: Faint arcs must be visible to show that you have used the correct method and not just a protractor.
- Neatness: The drawing should be clean, with sharp pencil lines and clear labelling of points.
- Steps of Construction: Writing the steps is often required and carries specific marks.
3. What kind of short-answer or 1-mark questions can be expected from this chapter?
While this is a practical chapter, some theoretical short-answer questions are often asked. For the 2025-26 session, expect questions like:
- What are the essential instruments in a geometry box for constructions?
- What is the first step to construct a 90° angle?
- What does it mean to bisect a line segment?
- If you bisect a 90° angle, what is the measure of the two resulting angles?
4. Why is using only a ruler and compass important for constructions, even when a protractor seems easier?
This is a key conceptual point. Using only a ruler and compass forces you to rely on pure geometric principles and logic, not just measurement. These classical constructions are based on the foundational axioms of geometry. A protractor is a measuring device, while a compass helps create circles and arcs of specific radii, which are the building blocks of logical geometric proofs. Excelling at this demonstrates a deeper understanding of geometric relationships rather than just an ability to measure.
5. What are the most common mistakes students make in construction questions that lead to a loss of marks?
To avoid losing marks, be careful of these common errors:
- Using a thick or blunt pencil, which leads to inaccurate lines.
- Erasing the construction arcs, which are necessary proof of your method.
- A loose compass screw, which can cause the radius to change midway through an arc.
- Incorrectly labelling the points, lines, and angles in the final diagram.
- Forgetting to write the steps of construction when they are asked for.
6. How does understanding angle bisection help in constructing more complex angles like 45° or 22.5°?
Angle bisection is a fundamental technique that allows you to build other angles. The logic works in steps:
- First, you construct a standard angle, like 90° (by bisecting a straight line and constructing a perpendicular).
- Then, you bisect the 90° angle to get a perfect 45° angle.
- If you need an even smaller angle like 22.5°, you can simply bisect the 45° angle again.
7. Besides drawing them, what is the practical importance of a perpendicular bisector?
A perpendicular bisector is a very powerful tool in geometry. Every point on the perpendicular bisector of a line segment is equidistant from the two endpoints of that segment. This property is crucial for more advanced constructions, such as:
- Finding the centre of a circle that passes through three given points (the circumcenter of a triangle).
- Solving problems related to symmetry and reflection.
- Dividing a shape into two identical, mirror-image halves.
