Question 4
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?
When a paper is folded and a hole is punched, the fold line acts like a mirror. The hole appears on both sides of this mirror line. So, the fold line is a line of symmetry for the pattern of holes.
Step 1 — Figure (a) fold
Let us look at figure (a). It shows two holes. This means the paper was folded once. The line along which the paper was folded is the diagonal from top-left to bottom-right. When a paper is folded along this diagonal, and a hole is punched, the two holes will be mirror images across this diagonal line. So, this diagonal is the line of symmetry for the pattern.
Step 2 — Figure (b) fold
Let us look at figure (b). It shows two holes. This means the paper was folded once. The line along which the paper was folded is horizontally across the middle. When a paper is folded along this horizontal line, and a hole is punched, the two holes will be mirror images across this horizontal line. So, this horizontal line is the line of symmetry for the pattern.
Step 3 — Figure (c) fold
Let us look at figure (c). It shows two holes. This means the paper was folded once. The line along which the paper was folded is vertically down the middle. When a paper is folded along this vertical line, and a hole is punched, the two holes will be mirror images across this vertical line. So, this vertical line is the line of symmetry for the pattern.
Step 4 — Figure (d) fold
Let us look at figure (d). It shows four holes, one in each corner. To get four holes from a single punch, the paper must be folded twice. The line along which the paper was folded is diagonally. This means the paper was folded along both diagonals. First, fold the paper along one diagonal. Then, fold the paper again along the other diagonal. This folds the square into a small triangle. The four corners of the original square meet at the center of this folded triangle. If a hole is punched at this center point, it will go through all four layers of paper. When the paper is unfolded, the hole will appear in all four corners of the square.
Answer
(a) Folded diagonally from top-left to bottom-right. (b) Folded horizontally across the middle. (c) Folded vertically down the middle. (d) Folded diagonally.
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°?