Question 3
Punching Game
The fold is a line of symmetry. Punch holes at different locations of a folded square sheet of paper using a punching machine and create different symmetric patterns.
When we fold a paper, the fold line becomes a line of symmetry.
Step 1 — Folding the Paper
We start with a square sheet of paper. We fold it exactly in half. The fold creates a straight line. This line is the line of symmetry. Look at the first picture.
Step 2 — Punching a Hole
Next, we use a punching machine. We punch a hole through the folded paper. The punch goes through two layers of paper. These two layers are mirror images. The hole is not on the fold line. Look at the second picture.
Step 3 — Unfolding the Paper
Now, we carefully unfold the paper. We will see two holes. Each hole is a mirror image. They are on opposite sides of the fold. The fold line is exactly between them. This creates a symmetric pattern. Look at the third picture.
Answer
(i) The fold line acts as a line of symmetry. (ii) Punching one hole creates two holes. (iii) The two holes form a symmetric pattern.
More questions in FIO
Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?
For each of the following figures, identify the line(s) of symmetry if it exists.
Punching Game
The fold is a line of symmetry. Punch holes at different locations of a folded square sheet of paper using a punching machine and create different symmetric patterns.
In each of the following figures, a hole was punched in a folded square sheet of paper and then the paper was unfolded. Identify the line along which the paper was folded. Figure (d) was created by punching a single hole. How was the paper folded?
Given the line(s) of symmetry, find the other hole(s):
Here are some questions on paper cutting. Consider a vertical fold. We represent it this way:
Vertical Fold
Similarly, a horizontal fold is represented as follows:
Horizontal Fold
After each of the following cuts, predict the shape of the hole when the paper is opened. After you have made your prediction, make the cutouts and verify your answer.
Trace each figure and draw the lines of symmetry, if any:
Copy the following on a dot grid. For each figure draw two more lines to make a shape that has a line of symmetry.
Find the angles of symmetry for the given figures about the point marked •.
(a) (b) (c)
Which of the following figures have more than one angle of symmetry?
Give the order of rotational symmetry for each figure:
Colour the sectors of the circle below so that the figure has:
(i) 3 angles of symmetry
(ii) 4 angles of symmetry
(iii) What are the possible numbers of angles of symmetry you can obtain by colouring the sectors in different ways?
Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.
Draw, wherever possible, a rough sketch of:
a. A triangle with at least two lines of symmetry and at least two angles of symmetry.
b. A triangle with only one line of symmetry but not having rotational symmetry.
c. A quadrilateral with rotational symmetry but no reflection symmetry.
d. A quadrilateral with reflection symmetry but not having rotational symmetry.
In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?
In a figure, 60° is an angle of symmetry. The figure has two angles of symmetry less than 60°. What is its smallest angle of symmetry?
Can we have a figure with rotational symmetry whose smallest angle of symmetry is:
a. 45°?
b. 17°?