NCERT Textbook: Symmetrical Designs | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

 Page 1


Chapter Chapter
10 10
Prem and Manu want to paste ‘Happy Birthday’ cutouts on a wall for Lali’s 
birthday. While preparing cutouts of letters, they observe that some letters 
can be cut out in an easy way. 
They remember that they learnt about reflection symmetry and lines of 
symmetry in Grade 4. They used their knowledge of lines of symmetry to 
make the cutouts. The letter A has a vertical line of symmetry. So, to cut 
out the letter ‘A’—
1. Fold a paper in half.
2. Draw half of the letter A along the fold.
3. Cut along the outline.
4. Open the paper to see the full letter A.
Alphabet Cutout
Step 1
Step 1 Step 2
Step 3 Step 4
Step 3
Step 2
Step 4
The letter H has two lines of symmetry.
1. Fold the paper into one-fourth (once 
vertically, once horizontally).
2. Draw one-fourth of the letter H along the 
fold.
3. Cut along the outline.
4. Open the paper to see the full letter H.
Which of the following alphabet cutouts can be made by just drawing half (
1
2 
) 
or quarter (
1
4 
) of the letter? You can do it by drawing lines of symmetry on 
the letters.
E N X T K V O
Which of the letters have a horizontal line of symmetry? _________________
Which of the letters have a vertical line of symmetry? ____________________
Which letters have both vertical and horizontal lines of symmetry?________
Let Us Do
Use lines of symmetry to make paper cutouts of diya, boat, and other 
designs. Look along the border of the page to find the pictures.
Symmetrical 
Designs
Chapter-10 Symmetrical Design.indd   136 Chapter-10 Symmetrical Design.indd   136 7/2/2025   6:31:14 PM 7/2/2025   6:31:14 PM
Page 2


Chapter Chapter
10 10
Prem and Manu want to paste ‘Happy Birthday’ cutouts on a wall for Lali’s 
birthday. While preparing cutouts of letters, they observe that some letters 
can be cut out in an easy way. 
They remember that they learnt about reflection symmetry and lines of 
symmetry in Grade 4. They used their knowledge of lines of symmetry to 
make the cutouts. The letter A has a vertical line of symmetry. So, to cut 
out the letter ‘A’—
1. Fold a paper in half.
2. Draw half of the letter A along the fold.
3. Cut along the outline.
4. Open the paper to see the full letter A.
Alphabet Cutout
Step 1
Step 1 Step 2
Step 3 Step 4
Step 3
Step 2
Step 4
The letter H has two lines of symmetry.
1. Fold the paper into one-fourth (once 
vertically, once horizontally).
2. Draw one-fourth of the letter H along the 
fold.
3. Cut along the outline.
4. Open the paper to see the full letter H.
Which of the following alphabet cutouts can be made by just drawing half (
1
2 
) 
or quarter (
1
4 
) of the letter? You can do it by drawing lines of symmetry on 
the letters.
E N X T K V O
Which of the letters have a horizontal line of symmetry? _________________
Which of the letters have a vertical line of symmetry? ____________________
Which letters have both vertical and horizontal lines of symmetry?________
Let Us Do
Use lines of symmetry to make paper cutouts of diya, boat, and other 
designs. Look along the border of the page to find the pictures.
Symmetrical 
Designs
Chapter-10 Symmetrical Design.indd   136 Chapter-10 Symmetrical Design.indd   136 7/2/2025   6:31:14 PM 7/2/2025   6:31:14 PM
137
Lali makes firkis for her friends. Follow the steps given below to make your 
own firki.
1. Take a square paper.
2. Fold the paper in half diagonally to make two triangles.
3. Open and fold it the other way to make two more triangles.
4. Open it again. You will see an ‘X’ shape on the paper.
5.  Use scissors to cut along the four lines of the ‘X’. Stop cutting  
about halfway to the centre.
6.  Take one corner of each triangle and fold it gently towards the  
centre of the paper. Do not press it flat.
7. Fold every other corner towards the centre.
8.  Push a pin through the folded corners and the centre of the  
paper.
9. Push the pin through a stick or straw.
Let Us Make a Windmill Firki
Observe the dot in the firki. Does the firki look the same after 
1
4 
, 
1
2 
, 
3
4 
, and a 
full turn? ___________________.
Make sure the pin is not too tight.
Check if your windmill spins when the wind is blowing.
Initial 
position
 
1
4 
 turn 
1
2 
 turn 
3
4 
 turn Full turn
Chapter-10 Symmetrical Design.indd   137 Chapter-10 Symmetrical Design.indd   137 7/2/2025   6:31:15 PM 7/2/2025   6:31:15 PM
Page 3


Chapter Chapter
10 10
Prem and Manu want to paste ‘Happy Birthday’ cutouts on a wall for Lali’s 
birthday. While preparing cutouts of letters, they observe that some letters 
can be cut out in an easy way. 
They remember that they learnt about reflection symmetry and lines of 
symmetry in Grade 4. They used their knowledge of lines of symmetry to 
make the cutouts. The letter A has a vertical line of symmetry. So, to cut 
out the letter ‘A’—
1. Fold a paper in half.
2. Draw half of the letter A along the fold.
3. Cut along the outline.
4. Open the paper to see the full letter A.
Alphabet Cutout
Step 1
Step 1 Step 2
Step 3 Step 4
Step 3
Step 2
Step 4
The letter H has two lines of symmetry.
1. Fold the paper into one-fourth (once 
vertically, once horizontally).
2. Draw one-fourth of the letter H along the 
fold.
3. Cut along the outline.
4. Open the paper to see the full letter H.
Which of the following alphabet cutouts can be made by just drawing half (
1
2 
) 
or quarter (
1
4 
) of the letter? You can do it by drawing lines of symmetry on 
the letters.
E N X T K V O
Which of the letters have a horizontal line of symmetry? _________________
Which of the letters have a vertical line of symmetry? ____________________
Which letters have both vertical and horizontal lines of symmetry?________
Let Us Do
Use lines of symmetry to make paper cutouts of diya, boat, and other 
designs. Look along the border of the page to find the pictures.
Symmetrical 
Designs
Chapter-10 Symmetrical Design.indd   136 Chapter-10 Symmetrical Design.indd   136 7/2/2025   6:31:14 PM 7/2/2025   6:31:14 PM
137
Lali makes firkis for her friends. Follow the steps given below to make your 
own firki.
1. Take a square paper.
2. Fold the paper in half diagonally to make two triangles.
3. Open and fold it the other way to make two more triangles.
4. Open it again. You will see an ‘X’ shape on the paper.
5.  Use scissors to cut along the four lines of the ‘X’. Stop cutting  
about halfway to the centre.
6.  Take one corner of each triangle and fold it gently towards the  
centre of the paper. Do not press it flat.
7. Fold every other corner towards the centre.
8.  Push a pin through the folded corners and the centre of the  
paper.
9. Push the pin through a stick or straw.
Let Us Make a Windmill Firki
Observe the dot in the firki. Does the firki look the same after 
1
4 
, 
1
2 
, 
3
4 
, and a 
full turn? ___________________.
Make sure the pin is not too tight.
Check if your windmill spins when the wind is blowing.
Initial 
position
 
1
4 
 turn 
1
2 
 turn 
3
4 
 turn Full turn
Chapter-10 Symmetrical Design.indd   137 Chapter-10 Symmetrical Design.indd   137 7/2/2025   6:31:15 PM 7/2/2025   6:31:15 PM
138
Observe the letters below. Do they look the same when turned? Dots have 
been marked on the letters to keep track of the orientation of letters. You may 
also cut out the letters and fix the centre point of the letter by a nail or use 
a tracing paper to check if the letter looks the same when turned.
Original 
letter
1
4
 turn
1
2
 turn
3
4
 turn
Full turn
Rotational 
symmetry  
(Yes/No)
Yes, at 
1
2
 turn
Which digit(s) have reflection symmetry? ___________________________
Which digit(s) have rotational symmetry? ___________________________
Which digit(s) have both rotational and reflection symmetries? ________
Now, let us look at the following numbers: 
||
, 
|
00
|
 
Do these have (a) rotational symmetry, (b) reflection symmetry or (c) both 
symmetries?
Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry, 
reflection symmetry, or both.
The letter H has rotational symmetry, as it looks the same when 
rotated by half a turn.
A firki has rotational symmetry, as it looks the same when rotated 
by 
1
4
, 
1
2
, and 
3
4
 turn.
Let Us Do
Find symmetry in the digits.
Chapter-10 Symmetrical Design.indd   138 Chapter-10 Symmetrical Design.indd   138 04-07-2025   12:20:00 04-07-2025   12:20:00
Page 4


Chapter Chapter
10 10
Prem and Manu want to paste ‘Happy Birthday’ cutouts on a wall for Lali’s 
birthday. While preparing cutouts of letters, they observe that some letters 
can be cut out in an easy way. 
They remember that they learnt about reflection symmetry and lines of 
symmetry in Grade 4. They used their knowledge of lines of symmetry to 
make the cutouts. The letter A has a vertical line of symmetry. So, to cut 
out the letter ‘A’—
1. Fold a paper in half.
2. Draw half of the letter A along the fold.
3. Cut along the outline.
4. Open the paper to see the full letter A.
Alphabet Cutout
Step 1
Step 1 Step 2
Step 3 Step 4
Step 3
Step 2
Step 4
The letter H has two lines of symmetry.
1. Fold the paper into one-fourth (once 
vertically, once horizontally).
2. Draw one-fourth of the letter H along the 
fold.
3. Cut along the outline.
4. Open the paper to see the full letter H.
Which of the following alphabet cutouts can be made by just drawing half (
1
2 
) 
or quarter (
1
4 
) of the letter? You can do it by drawing lines of symmetry on 
the letters.
E N X T K V O
Which of the letters have a horizontal line of symmetry? _________________
Which of the letters have a vertical line of symmetry? ____________________
Which letters have both vertical and horizontal lines of symmetry?________
Let Us Do
Use lines of symmetry to make paper cutouts of diya, boat, and other 
designs. Look along the border of the page to find the pictures.
Symmetrical 
Designs
Chapter-10 Symmetrical Design.indd   136 Chapter-10 Symmetrical Design.indd   136 7/2/2025   6:31:14 PM 7/2/2025   6:31:14 PM
137
Lali makes firkis for her friends. Follow the steps given below to make your 
own firki.
1. Take a square paper.
2. Fold the paper in half diagonally to make two triangles.
3. Open and fold it the other way to make two more triangles.
4. Open it again. You will see an ‘X’ shape on the paper.
5.  Use scissors to cut along the four lines of the ‘X’. Stop cutting  
about halfway to the centre.
6.  Take one corner of each triangle and fold it gently towards the  
centre of the paper. Do not press it flat.
7. Fold every other corner towards the centre.
8.  Push a pin through the folded corners and the centre of the  
paper.
9. Push the pin through a stick or straw.
Let Us Make a Windmill Firki
Observe the dot in the firki. Does the firki look the same after 
1
4 
, 
1
2 
, 
3
4 
, and a 
full turn? ___________________.
Make sure the pin is not too tight.
Check if your windmill spins when the wind is blowing.
Initial 
position
 
1
4 
 turn 
1
2 
 turn 
3
4 
 turn Full turn
Chapter-10 Symmetrical Design.indd   137 Chapter-10 Symmetrical Design.indd   137 7/2/2025   6:31:15 PM 7/2/2025   6:31:15 PM
138
Observe the letters below. Do they look the same when turned? Dots have 
been marked on the letters to keep track of the orientation of letters. You may 
also cut out the letters and fix the centre point of the letter by a nail or use 
a tracing paper to check if the letter looks the same when turned.
Original 
letter
1
4
 turn
1
2
 turn
3
4
 turn
Full turn
Rotational 
symmetry  
(Yes/No)
Yes, at 
1
2
 turn
Which digit(s) have reflection symmetry? ___________________________
Which digit(s) have rotational symmetry? ___________________________
Which digit(s) have both rotational and reflection symmetries? ________
Now, let us look at the following numbers: 
||
, 
|
00
|
 
Do these have (a) rotational symmetry, (b) reflection symmetry or (c) both 
symmetries?
Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry, 
reflection symmetry, or both.
The letter H has rotational symmetry, as it looks the same when 
rotated by half a turn.
A firki has rotational symmetry, as it looks the same when rotated 
by 
1
4
, 
1
2
, and 
3
4
 turn.
Let Us Do
Find symmetry in the digits.
Chapter-10 Symmetrical Design.indd   138 Chapter-10 Symmetrical Design.indd   138 04-07-2025   12:20:00 04-07-2025   12:20:00
139
Colour the square given in the adjoining figure using 
two colours so that the design looks the same after 
every 
1
4
 turn.
How many times does this shape look the same during 
a full turn?
(a) Does the design have rotational symmetry? 
Yes/No.
(b) Try to change the design by adding some 
shape(s) so that the new design looks the 
same after a 
1
2
 turn. Draw the new design in 
your notebook.
(c) Now try to modify or add more shapes so that the new design looks the 
same after 
1
4
 turn. Draw the new design in your notebook.
(d) Do the new designs have reflection symmetry? If yes, draw the lines of 
symmetry.
Making Designs
Let Us Think
Does this design look the same after 
1
2
 turn? __________
Does the design look the same after 
1
4
 turn?__________
Cut out squares and equilateral 
triangles with the same side 
length. These are provided at the 
end of the book. 
Make different symmetrical 
designs by using these two shapes.
Do these designs have reflection symmetry also? Draw the line(s) of 
symmetry.
Let Us Do
Chapter-10 Symmetrical Design.indd   139 Chapter-10 Symmetrical Design.indd   139 7/2/2025   6:31:15 PM 7/2/2025   6:31:15 PM
Page 5


Chapter Chapter
10 10
Prem and Manu want to paste ‘Happy Birthday’ cutouts on a wall for Lali’s 
birthday. While preparing cutouts of letters, they observe that some letters 
can be cut out in an easy way. 
They remember that they learnt about reflection symmetry and lines of 
symmetry in Grade 4. They used their knowledge of lines of symmetry to 
make the cutouts. The letter A has a vertical line of symmetry. So, to cut 
out the letter ‘A’—
1. Fold a paper in half.
2. Draw half of the letter A along the fold.
3. Cut along the outline.
4. Open the paper to see the full letter A.
Alphabet Cutout
Step 1
Step 1 Step 2
Step 3 Step 4
Step 3
Step 2
Step 4
The letter H has two lines of symmetry.
1. Fold the paper into one-fourth (once 
vertically, once horizontally).
2. Draw one-fourth of the letter H along the 
fold.
3. Cut along the outline.
4. Open the paper to see the full letter H.
Which of the following alphabet cutouts can be made by just drawing half (
1
2 
) 
or quarter (
1
4 
) of the letter? You can do it by drawing lines of symmetry on 
the letters.
E N X T K V O
Which of the letters have a horizontal line of symmetry? _________________
Which of the letters have a vertical line of symmetry? ____________________
Which letters have both vertical and horizontal lines of symmetry?________
Let Us Do
Use lines of symmetry to make paper cutouts of diya, boat, and other 
designs. Look along the border of the page to find the pictures.
Symmetrical 
Designs
Chapter-10 Symmetrical Design.indd   136 Chapter-10 Symmetrical Design.indd   136 7/2/2025   6:31:14 PM 7/2/2025   6:31:14 PM
137
Lali makes firkis for her friends. Follow the steps given below to make your 
own firki.
1. Take a square paper.
2. Fold the paper in half diagonally to make two triangles.
3. Open and fold it the other way to make two more triangles.
4. Open it again. You will see an ‘X’ shape on the paper.
5.  Use scissors to cut along the four lines of the ‘X’. Stop cutting  
about halfway to the centre.
6.  Take one corner of each triangle and fold it gently towards the  
centre of the paper. Do not press it flat.
7. Fold every other corner towards the centre.
8.  Push a pin through the folded corners and the centre of the  
paper.
9. Push the pin through a stick or straw.
Let Us Make a Windmill Firki
Observe the dot in the firki. Does the firki look the same after 
1
4 
, 
1
2 
, 
3
4 
, and a 
full turn? ___________________.
Make sure the pin is not too tight.
Check if your windmill spins when the wind is blowing.
Initial 
position
 
1
4 
 turn 
1
2 
 turn 
3
4 
 turn Full turn
Chapter-10 Symmetrical Design.indd   137 Chapter-10 Symmetrical Design.indd   137 7/2/2025   6:31:15 PM 7/2/2025   6:31:15 PM
138
Observe the letters below. Do they look the same when turned? Dots have 
been marked on the letters to keep track of the orientation of letters. You may 
also cut out the letters and fix the centre point of the letter by a nail or use 
a tracing paper to check if the letter looks the same when turned.
Original 
letter
1
4
 turn
1
2
 turn
3
4
 turn
Full turn
Rotational 
symmetry  
(Yes/No)
Yes, at 
1
2
 turn
Which digit(s) have reflection symmetry? ___________________________
Which digit(s) have rotational symmetry? ___________________________
Which digit(s) have both rotational and reflection symmetries? ________
Now, let us look at the following numbers: 
||
, 
|
00
|
 
Do these have (a) rotational symmetry, (b) reflection symmetry or (c) both 
symmetries?
Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry, 
reflection symmetry, or both.
The letter H has rotational symmetry, as it looks the same when 
rotated by half a turn.
A firki has rotational symmetry, as it looks the same when rotated 
by 
1
4
, 
1
2
, and 
3
4
 turn.
Let Us Do
Find symmetry in the digits.
Chapter-10 Symmetrical Design.indd   138 Chapter-10 Symmetrical Design.indd   138 04-07-2025   12:20:00 04-07-2025   12:20:00
139
Colour the square given in the adjoining figure using 
two colours so that the design looks the same after 
every 
1
4
 turn.
How many times does this shape look the same during 
a full turn?
(a) Does the design have rotational symmetry? 
Yes/No.
(b) Try to change the design by adding some 
shape(s) so that the new design looks the 
same after a 
1
2
 turn. Draw the new design in 
your notebook.
(c) Now try to modify or add more shapes so that the new design looks the 
same after 
1
4
 turn. Draw the new design in your notebook.
(d) Do the new designs have reflection symmetry? If yes, draw the lines of 
symmetry.
Making Designs
Let Us Think
Does this design look the same after 
1
2
 turn? __________
Does the design look the same after 
1
4
 turn?__________
Cut out squares and equilateral 
triangles with the same side 
length. These are provided at the 
end of the book. 
Make different symmetrical 
designs by using these two shapes.
Do these designs have reflection symmetry also? Draw the line(s) of 
symmetry.
Let Us Do
Chapter-10 Symmetrical Design.indd   139 Chapter-10 Symmetrical Design.indd   139 7/2/2025   6:31:15 PM 7/2/2025   6:31:15 PM
140
Now, make your designs. Sort your designs in 3 categories — designs with 
only rotational symmetry, designs with only reflection symmetry, and 
designs with both rotational and reflection symmetry.
Let Us Explore
Block printing is a traditional craft of  
Rajasthan, known for beautiful patterns and 
bright colours. 
Artisans use carved wooden blocks to print 
designs on fabric. 
This art has been practised for centuries and 
makes Rajasthan’s textiles special.
Does this shape have reflection symmetry? 
If yes, draw its line(s) of symmetry. 
Does it have rotational symmetry? 
If yes, at which turn? 
Does it have both symmetries?
Below are images of wooden blocks and a part of their prints. Match each 
block to its correct print by drawing a line. One is done for you.
Wooden Block Print
(i) (ii) (iii) (iv) (v)
(a) (b) (c) (d) (e)
Chapter-10 Symmetrical Design.indd   140 Chapter-10 Symmetrical Design.indd   140 7/2/2025   6:31:21 PM 7/2/2025   6:31:21 PM