Symmetry

Here’s a summary of the chapter “Symmetry” typically found in Grade 6 Maths:

Concept: Symmetry refers to a figure having two identical halves when folded along a line. Imagine folding a paper in half and getting two matching shapes on either side.

Types of Symmetry:

• Line Symmetry (Bilateral Symmetry): This is the most common type. A figure has one line (axis of symmetry) where you can fold it and get two matching halves. Examples include a butterfly, a rectangle, or a letter “H.”
• Rotational Symmetry: A figure has rotational symmetry if it can be rotated a certain angle and look exactly the same. Examples include a circle, a square (with 90-degree rotations), or a snowflake (with 60-degree rotations).

Identifying Symmetry:

• The chapter teaches methods to identify whether a shape has symmetry and what type of symmetry it has. This often involves drawing fold lines or visualizing rotations.

Applications of Symmetry:

• Symmetry is found everywhere in nature, art, and design. The chapter might introduce students to how symmetry is used in creating patterns, designing buildings, or understanding certain natural objects.
• The concept of reflection can be introduced in relation to symmetry. Imagine a mirror image of a shape – that’s a reflectional symmetry.

Learning Activities:

• The chapter might include activities like:
  • Identifying symmetrical shapes from drawings or real objects.
  • Completing patterns based on symmetry.
  • Drawing shapes with specific types of symmetry.
  • Exploring symmetry in everyday objects like toys, flowers, or buildings.

Exercise 13.1

1. List any four symmetrical objects from your home or school.

Ans : 

Book

Plate

Pencil

Window

2. For the given figure, which one is the mirror line, l1 or l2?

Ans : 

Based on the image, the mirror line is l2.

3. Identify the shapes given below. Check whether they are symmetrical or not. Draw the line of symmetry as well.

Ans : 

(a) The given symmetric figure is a lock in which vertical line ‘l’ is the line of symmetry.

(b) The given figure is a symmetrical bucket in which vertical line ‘l’ is the line of symmetry.

(c) The given figure is not symmetrical.

(d) The given figure is a symmetric telephone in which vertical line l is called the line of symmetry.

(e) The given figure is symmetrical. Horizontal line l is called the line of symmetry.

(f) The given figure is symmetrical. Vertical line l is called its line of symmetry.

4. Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook is earlier classes. Then complete them such that the dotted line is the line of symmetry.

Ans :

5. In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.

Ans : 

The completed figure is as follows:

6. In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric.

Ans :
The symmetric figure is given as follows.

Exercise 13.2

1. Find the number of lines of symmetry for each of the following shapes.

Ans : 

(a) Here, there are four symmetric lines l, m, n and o.

(b) In this figure, there are four symmetric lines p, q, r and s.

(c) In this shape, u, v , w and x are four lines of symmetry.

(d) In this shape only m is the line of symmetry.

(e) Here, a, b, c, d, e and fare six lines of symmetry.

(f) In this figure l, m, n, o, p and q are six lines of symmetry.

(g) This figure has no lines of symmetry.

(h) This figure has no lines of symmetry.

(i) This figure has five lines of symmetry.

2. Copy the triangle in each of the figures on squared paper. In each case, draw the line(s) of symmetry, if any and identify the type of triangle. (Some of you may like to trace the figures and try paper-folding first!)

Ans : 

(a) It is an isosceles triangle having one symmetric line.

(b) This figure is an isosceles triangle having only one symmetric line.

(c) It is an isosceles right angled triangle which has only one symmetric line.

(d) It is a scalene triangle. It has no symmetric line.

3. Complete the following table.

Shape	Rough figure	Number of lines of symmetry
Equilateral triangle		3
Square
Rectangle
Isosceles triangle
Rhombus
Circle

Ans : 

Shape	Rough figure	Number of lines of symmetry
(a) Equilateral triangle		3
(b) Square		4
(c) Rectangle		2
(d) Isosceles triangle		1
(e) Rhombus		2
(f) Circle		Infinite

4. Can you draw a triangle which has

(a) exactly one line of symmetry?

(b) exactly two lines of symmetry?

(c) exactly three lines of symmetry?

(d) no lings of symmetry?

Sketch a rough figure in each case.

Ans : 

(a) Yes, Isosceles right angled triangle has exactly one line of symmetry.

(b) No, we cannot draw any triangle with two symmetric lines.

(c) Yes, equilateral triangle has three lines of symmetry.

(d) Yes, Scalene triangle has no lines of symmetry

5. On a squared paper, sketch the following:

(а) A triangle with a horizontal line of symmetry but no vertical line of symmetry.

(b) A quadrilateral with both horizontal and vertical lines of symmetry.

(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

(d) A hexagon with exactly two lines of symmetry.

(e) A hexagon with six lines of symmetry. (Hint: It will be helpful if you first draw the lines of symmetry and then complete the figures)

Ans : 

(a) The figure shows an isosceles triangle with horizontal line of symmetry.

(b) Rectangle (quadrilateral) shows both the horizontal and vertical lines of symmetry.

(c) Trapezium (quadrilateral) shows the horizontal but no vertical line of symmetry.

(d) The hexagon drawn below shows only two lines of symmetry.

(e) The regular hexagon shows the six lines of symmetry.

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

Ans : 

(a) The given figure has no line of symmetry as it is not symmetrical.

(b) The given figure has two lines of symmetry.

(c) The given figure has four lines of symmetry.

(d) The given figure has two lines of symmetry.

(e) This figure has only one horizontal line of symmetry.

(f) The given figure has two lines of symmetry.

7. Consider the letters of English alphabets A to Z. List among them the letters which have

(a) vertical lines of symmetry, (like A)

(b) horizontal lines of symmetry (like B)

(c) no lines of symmetry, (like Q)

Ans : 

(a) Vertical Lines of Symmetry:

• A
• H
• I
• M
• O
• T
• U
• V
• W
• X
• Y

(b) Horizontal Lines of Symmetry:

• B
• C
• D
• E 
• H 
• I
• K
• O
• X 

(c) No Lines of Symmetry:

• F
• G
• J
• L
• N
• P
• Q
• R
• S
• Z

8. Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.

Ans : 

The given figures will be seen as follows when they are completed.

Exercise 13.3 

1. Find the number of lines of symmetry in each of the following shapes. How will you check your answer?

Ans : (a) The given figure has 4 lines of symmetry.

(b) The given figure has only one line of symmetry.

(c) The given figure has two line of symmetry.

(d) The given figure has two lines of symmetry.

(e) This figure has only one line of symmetry.

(f) The given figure has two lines of symmetry.

2. Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has two dotted lines as two lines of symmetry.

Ans : 

3. In each figure alongside, a letter of the alphabet is shown along with a vertical line. Take the mirror image of the letter in the given line. Find which letters look the same after reflection (i.e. which letters look the same in the image) and which do not. Can you guess why?

Try for OEM NPHLTSVX

Ans :