Question 4
Construct
1. A Person
How will you draw this?
To construct the figure of a person, combine simple geometric elements in order:
- A circle for the head (drawn with a compass).
- A vertical line for the neck.
- A curve for the shoulders/top of the body.
- Straight line segments for the sides and base of the torso.
Step 1 · Draw the Head
Using a compass, draw a circle to represent the head.
Step 2 · Draw the Neck
Draw a short vertical straight line extending downwards from the bottom of the circle.
Step 3 · Draw the Top Curve of the Body
Draw a curved line below the neck that dips downwards in the middle, ensuring the neck line touches its midpoint.
Step 4 · Draw the Sides and Base of the Body
- Draw two vertical lines of equal length downwards from both ends of the curved line.
- Join the bottom endpoints of these two lines with a horizontal straight line to complete the figure.
Follow the construction steps given above to draw the person using a compass and a ruler.
- Asymmetric Body Sides: Drawing the two vertical side lines of unequal length leads to an uneven torso.
- Freehand Circles: Drawing the circular head freehand instead of using a compass can result in an irregular shape.
More questions in A
Observe the following figures and try drawing them freehand.
Mark a point in your notebook. Then, mark as many points as possible, in different directions, that are away from .
Think: Imagine marking all the points of distance from the point . 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 are indeed . 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 from 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?