Question 3
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?
We will use a compass. We will draw circles. We will combine them. This makes the figures.
Step 1 — Two touching circles
Let us draw a circle. We choose a radius. We place the compass point on its edge. We draw another circle. We use the same radius.
Step 2 — Concentric circles
Let us draw a circle. We choose a center point. We keep the compass point there. We adjust the compass. We make the radius smaller. We draw a second circle.
Step 3 — Three overlapping circles
Let us draw a first circle. We place the compass point on its edge. We draw a second circle. It overlaps the first. We place the compass point on the second circle's edge. We draw a third circle. It overlaps the second.
Step 4 — Mickey Mouse face
Let us draw a large circle. This is for the face. We place the compass point on its top edge. We draw a smaller circle. This is one ear. We repeat for the other ear. We draw two small circles for eyes. We draw a tiny circle for the nose. We draw a short line for the mouth.
Step 5 — Crossed lines with circles
Let us draw two straight lines. They cross each other. We use a ruler for this. We place the compass point at one line's end. We draw a small circle. We repeat for the other line's end.
Answer
(i) Yes, instruments make construction easier. (ii) They help us draw perfect circles. (iii) They also help us draw straight lines.
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?