Playing with Constructions | A

Question 1

Observe the following figures and try drawing them freehand.

Question diagram 1
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Solution
Understand the Question
  • Freehand drawing means sketching shapes by hand smoothly without using instruments like a compass or ruler.
  • Observe the given figures to identify their basic components—such as circles, lines, and dots—and their relationships (touching, overlapping, concentric, or intersecting).

Step 1 · Draw Two Touching Circles

Draw one circle, then draw a second circle of equal size right next to it so they touch externally at a single point without overlapping.

Step 2 · Draw Three Overlapping Circles

Draw three circles in a horizontal row such that each circle partially overlaps with the next one.

Step 3 · Draw Concentric Circles

Draw a larger outer circle, and then draw a smaller circle inside it sharing the same center point.

Step 4 · Draw the Circle-Based Face Figure

  1. Draw a large circle for the head.
  2. Add two small circles on the top-left and top-right for the ears.
  3. Draw two small circles inside with dots for the eyes.
  4. Add a small dot for the nose and a short line for the mouth.

Step 5 · Draw Crossed Lines with Circles

Draw two straight lines intersecting in an 'X' shape, then add a small circle at each of the two bottom ends.

Answer

All the given figures are drawn freehand by following their geometric shapes and relative positions.

Common Mistakes
  • Using Geometric Tools: Using a compass or ruler instead of practicing freehand sketching by hand.
  • Hesitant Stroke Movement: Drawing small, broken, sketchy lines instead of practicing smooth, continuous circular motions with a relaxed pencil grip.

More questions in A

Q1

Observe the following figures and try drawing them freehand.

Q2

Mark a point PP in your notebook. Then, mark as many points as possible, in different directions, that are 4 cm4\text{ cm} away from PP.

Think: Imagine marking all the points of 4 cm4\text{ cm} distance from the point PP. 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 PP are indeed 4 cm4\text{ 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 cm4\text{ cm} from PP using the compass. How can this be done?

Q3

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?

Q4

Construct

1. A Person

How will you draw this?

Q5

2. Wavy Wave

Construct this.

Q6

Make other artwork of your choice with a ruler and a compass.

Q7

Explore

How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?

Q8

How will you record your observations? First, identify the parameters that need to be tracked. They are the sides of the rectangle and the 8 angles formed by the two diagonals. Are there any other measurements that you would want to keep track of?

Q9

In your experimentation, did you consider the case when all four sides of the rectangle are equal? That is, did you consider the case of a square? See what happens in this special case!

Q10

Math Talk

What general laws did you observe with respect to the angles and sides? Try to frame and discuss them with your classmates.

How can one be sure if the laws that you have observed will always be true?

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