CBSE Class 6 Maths Important Questions Chapter 8 - Playing with Constructions

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:

1. Start by sketching a rough diagram and marking the given measurements.

2. Draw a line segment AB of 6 cm.

3. At point A, use a protractor to draw a line AX perpendicular to AB.

4. With A as the centre, draw an arc with a radius of 4 cm to intersect AX at point D.

5. Now, with DD as the centre, draw an arc of a 6 cm radius above the line segment AB.

6. 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