Symmetry | FIO

Question 2

For each of the following figures, identify the line(s) of symmetry if it exists.

Question diagram 1
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Solution

FIO-2

Chapter: SYMMETRY
Class: 6 (Class 6)
Category: figure_it_out

Question

For each of the following figures, identify the line(s) of symmetry if it exists.

Question diagram(s):

Question diagram

A line of symmetry is a line that divides a figure into two identical halves. If we fold the figure along this line, both halves will match perfectly.

Step 1 — Figure (i) (Leftmost polygon)

Let us look at the first figure. This figure is an irregular shape. We try to draw a line to fold it. No line will make the two halves match. So, this figure has

no lines of symmetry\boxed{\text{no lines of symmetry}}

Diagram 1

Step 2 — Figure (ii) (Second polygon)

Let us look at the second figure. This figure is a quadrilateral. It looks like a kite shape. A kite has one line of symmetry. This line goes through its opposite corners. We can fold it along this line. The two halves will match perfectly. So, this figure has

1 line of symmetry\boxed{\text{1 line of symmetry}}

Diagram 2

Step 3 — Figure (iii) (Third polygon)

Let us look at the third figure. This figure is a trapezoid. It has two parallel sides. The other two sides are not parallel. We try to draw a line to fold it. No line will make the two halves match. So, this figure has

no lines of symmetry\boxed{\text{no lines of symmetry}}

Diagram 3

Step 4 — Figure (iv) (Fourth polygon)

Let us look at the fourth figure. This figure is an L-shape. It has many corners. We try to draw a line to fold it. No line will make the two halves match. So, this figure has

no lines of symmetry\boxed{\text{no lines of symmetry}}

Diagram 4

Step 5 — Figure (v) (Rightmost polygon)

Let us look at the fifth figure. This figure is a triangle. All its sides look different in length. This is called a scalene triangle. A scalene triangle has no lines of symmetry. So, this figure has

no lines of symmetry\boxed{\text{no lines of symmetry}}

Diagram 5

Answer

(i) The leftmost polygon has no lines of symmetry. (ii) The second polygon has 1 line of symmetry. (iii) The third polygon has no lines of symmetry. (iv) The fourth polygon has no lines of symmetry. (v) The rightmost polygon has no lines of symmetry.

More questions in FIO

Q1

Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?

Q2

For each of the following figures, identify the line(s) of symmetry if it exists.

Q3

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.

Q4

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?

Q5

Given the line(s) of symmetry, find the other hole(s):

Q6

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

Q7

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.

Q8

Trace each figure and draw the lines of symmetry, if any:

Q9

Copy the following on a dot grid. For each figure draw two more lines to make a shape that has a line of symmetry.

Q10

Find the angles of symmetry for the given figures about the point marked •.

(a) (b) (c)

Q11

Which of the following figures have more than one angle of symmetry?

Q12

Give the order of rotational symmetry for each figure:

Q13

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?

Q14

Draw two figures other than a circle and a square that have both reflection symmetry and rotational symmetry.

Q15

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.

Q16

In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?

Q17

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?

Q18

Can we have a figure with rotational symmetry whose smallest angle of symmetry is:

a. 45°?

b. 17°?

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