NCERT Book Class 6 Maths Playing with Constructions PDF Download

Chapter 8: Playing with Constructions

8.1 Artwork

Observe the following figures and try drawing them freehand.

[Figure 8.1: Various figures made of circles and geometric shapes, See in your textbook]

Now, arm yourself with a ruler and a compass. Let us explore if we can draw these figures with these tools and get familiar with a compass.

Observe the way a compass is made. What can one draw with the compass? Explore!

Do you know what curves are? They are any shapes that can be drawn on paper with a pencil, and include straight lines, circles and other figures as shown below:

[Figure: Examples of curves including wavy lines, a circle, a straight line, and an undulating curve, See in your textbook]

Mark a point 'P' in your notebook. Then, mark as many points as possible, in different directions, that are 4 cm away from P.

Think

Imagine marking all the points of 4 cm distance from the point P. How would they look?

Try to draw it and verify if it is correct by taking some points on the curve and checking if their distances from P are indeed 4 cm.

Explore, if you have not already done so, and see if a compass can be used for this purpose.

You can start by marking a few points of distance 4 cm from P using the compass. How can this be done?

[Figure: A diagram showing point P with points Q and R each at 4 cm distance, See in your textbook]

You will have to open up the compass against a ruler (see Fig. 8.2) such that the distance between the tip of the compass and the pencil is 4 cm.

Now, try to get the full curve.

Hint: Keep the point of the compass fixed moving only the pencil.

What is the shape of the curve? It is a circle!

Take a point on the circle. What will be its distance from P - equal to 4 cm, less than 4 cm or greater than 4 cm? Similarly, what will be the distance between P and another point on the circle?

As shown in the figure, the point P is called the centre of the circle and the distance between the centre and any point on the circle is called the radius of the circle.

[Figure 8.2: A compass positioned against a ruler showing the radius and centre of a circle being drawn, See in your textbook]

Teacher's Note

When you use a compass, the metal point stays exactly at the centre while the pencil rotates around it. This is why every point on the circle is the same distance away - they are all one radius length from the centre. If the radius is 4 cm, then every single point on the circle is 4 cm from P.

Having explored the use of a compass, go ahead and recreate the images in Fig. 8.1.

Can you make the figures look as good as the figures shown there? Try again if you want to!

Also, has the use of instruments made the construction easier?

Now try constructing the following figures.

Teacher's Note

Drawing freehand and drawing with instruments are two different skills. Freehand drawing helps you understand shapes, but instruments let you draw exactly. When you draw a circle freehand, you are guessing where the edge goes; with a compass, every point is precise because it is always the same distance from the centre.

Key Points

• A curve is any shape that can be drawn on paper with a pencil, including straight lines, circles, and other figures.
• A compass is a tool used to draw circles by keeping one point fixed at the centre while the pencil rotates around it.
• The centre of a circle is the fixed point, and the radius is the distance from the centre to any point on the circle.
• All points on a circle are the same distance (the radius) from the centre of the circle.

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