Question 1
Observe the following figures and try drawing them freehand.
We will learn to draw different shapes using circles and lines.
Step 1 — Look at the figures
We see many shapes.
All shapes use circles.
Some shapes use lines too.
Step 2 — Prepare your drawing tools
Get a pencil.
Get an eraser.
Get some paper.
Step 3 — Practice drawing circles
Try drawing many circles.
Make them different sizes.
Do not use a compass.
This helps your hand get steady.
Step 4 — Draw the first two circles
Draw one circle.
Draw another circle next to it.
Make them just touch each other.
Look at the top-left figure.
Step 5 — Draw the three overlapping circles
Draw three circles in a row.
Make each circle overlap the next one.
Look at the middle-left figure.
Step 6 — Draw the circle inside a circle
Draw a big circle.
Draw a smaller circle inside it.
Make sure their centers are the same.
Look at the top-right figure.
Step 7 — Draw the face
Draw a big circle for the head.
Draw two small circles for ears.
Place them on top of the head.
Draw two small circles for eyes.
Add tiny dots inside the eyes.
Draw a small dot for the nose.
Draw a short line for the mouth.
Look at the middle-right figure.
Step 8 — Draw the 'X' with circles
Draw two lines that cross.
Make them form an 'X' shape.
Draw a circle at the bottom-left end.
Draw another circle at the bottom-right end.
Look at the bottom figure.
Answer
We have observed the figures. We have practiced drawing them freehand.
More questions in A
Observe the following figures and try drawing them freehand.
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?
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?
Construct
1. A Person
How will you draw this?
2. Wavy Wave
Construct this.
Make other artwork of your choice with a ruler and a compass.
Explore
How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?
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?
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!
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?