Question 2
For each of the following figures, identify the line(s) of symmetry if it exists.
- A line of symmetry is a fold line that divides a figure into two identical halves that coincide exactly when folded along it.
- If no such line can be drawn for a figure, it has no line of symmetry.
(i) Figure (i) (Leftmost polygon)
Step 1 · Examine Figure (i)
This figure is an irregular polygon. No straight line can divide it into two identical halves that overlap perfectly when folded.
(i) No line of symmetry
(ii) Figure (ii) (Second polygon)
Step 1 · Examine Figure (ii)
This figure is a kite. It has vertical line of symmetry passing through its opposite vertices, dividing the figure into two matching halves.
(ii) line of symmetry
(iii) Figure (iii) (Third polygon)
Step 1 · Examine Figure (iii)
This figure is a trapezium with unequal non-parallel sides. No fold line can divide it into two congruent halves.
(iii) No line of symmetry
(iv) Figure (iv) (Fourth polygon)
Step 1 · Examine Figure (iv)
This figure is an asymmetrical L-shaped polygon. No line can be drawn to fold the shape into identical matching halves.
(iv) No line of symmetry
(v) Figure (v) (Rightmost polygon)
Step 1 · Examine Figure (v)
This figure is a scalene triangle with sides of different lengths. A scalene triangle has no lines of symmetry.
(v) No line of symmetry
- Trapezium Symmetry: Assuming all trapeziums have a line of symmetry. Only an isosceles trapezium has line of symmetry; a general trapezium has none.
- Triangle Types: Confusing scalene triangles (no lines of symmetry) with isosceles ( line) or equilateral triangles ( lines).
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, is the smallest angle of symmetry. What are the other angles of symmetry of this figure?
In a figure, is an angle of symmetry. The figure has two angles of symmetry less than . What is its smallest angle of symmetry?
Can we have a figure with rotational symmetry whose smallest angle of symmetry is:
a. ?
b. ?