Question 5
Given the line(s) of symmetry, find the other hole(s):
A line of symmetry acts like a mirror for a shape.
Step 1 — Understanding symmetry
A line of symmetry divides a shape into two equal halves. If we fold the shape along this line, both halves match perfectly. If there is a hole on one side, its mirror image is the other hole. We find the other hole by reflecting the given hole. The reflected hole is the same distance from the line. It is on the opposite side of the line.
Step 2 — Solving for figure a
Look at figure a. The shape is a square. The dashed line is a diagonal line of symmetry. There is one hole in the top-left part. We reflect this hole across the diagonal line. The new hole appears in the bottom-right part.
Step 3 — Solving for figure b
Look at figure b. The shape is a square. The dashed line is a horizontal line of symmetry. There is one hole in the bottom-right part. We reflect this hole across the horizontal line. The new hole appears in the top-right part.
Step 4 — Solving for figure c
Look at figure c. The shape is a triangle. The dashed line is a vertical line of symmetry. There is one hole on the left side. We reflect this hole across the vertical line. The new hole appears on the right side.
Step 5 — Solving for figure d
Look at figure d. The shape is a circle. The dashed line is a diagonal line of symmetry. There is one hole in the top-right part. We reflect this hole across the diagonal line. The new hole appears in the bottom-left part.
Step 6 — Solving for figure e
Look at figure e. The shape is a circle. The dashed line is a diagonal line of symmetry. There is one hole in the top-left part. We reflect this hole across the diagonal line. The new hole appears in the bottom-right part.
Answer
The other holes are found by reflecting the given holes. They are placed symmetrically across the dashed line(s). The completed diagrams show all the holes.
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°?