NCERT Solutions for Class 5 Maths Mela Chapter 10 Symmetrical Designs

NCERT Textbook Page 136

Alphabet Cutout

Which of the following alphabet cutouts can be made by just drawing half ($$\frac{1}{2}$$) or quarter ($$\frac{1}{4}$$) of the letter? You can do it by drawing lines of symmetry on the letters.

Solution:

Letters with ($$\frac{1}{4}$$) symmetry.

Letters with ($$\frac{1}{2}$$) symmetry.

Which of the letters have a horizontal line of symmetry? _________________

Solution:

Which of the letters have a vertical line of symmetry? ____________________

Solution:

Which letters have both vertical and horizontal lines of symmetry?________

Solution:

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 fine the pictures.

Solution:
Students should do it by themselves

NCERT Textbook Pages 137-138

Let Us Make a Windmill Firki

Observe the dot in the firki. Does the firki look the same after $$\frac{1}{4}, \frac{1}{2}, \frac{3}{4}$$ and a full turn?

Solution:

Yes

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 tracing paper to check if the letter looks the same when turned.

Solution:

NCERT Textbook Page 138

Let Us Do

Find symmetry in the digits.

Solution:

Horizontal line of symmetry.

Both horizontal and vertical line of symmetry

Which digit(s) have reflection symmetry?

Solution:

Which digit(s) have rotational symmetry?

Solution:

Which digit(s) have both rotational and reflection symmetries?

Solution:

Now, let us look at the following numbers: ||, |00|

Do these have

(a) rotational symmetry,
(b) reflection symmetry or
(c) both symmetries?

Solution:

Both || and |00| exhibit rotational symmetry as well as reflection symmetry.

Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry, reflection symmetry, or both.

Solution:

A 2-digit number that has both rotational and reflection symmetry is ||.

The 3-digit numbers that show both rotational and reflection symmetry are ||| and |0|.

The 4-digit numbers that have both rotational and reflection symmetry are |||| and |00|.

NCERT Textbook Page 139

Making Designs

(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 $$\frac{1}{2}$$ turn. Draw the new design 2 in your notebook.

Solution:
Students should do it by themselves.

(c) Now try to modify or add more shapes so that the new design looks the same after ~ turn.

Draw the new design in your notebook.

Solution:
Students should do it by themselves.

(d) Do the new designs have reflection symmetry? If yes, draw the lines of symmetry.

Solution:
Students should do it by themselves.

Let Us Think

Does this design look the same after $$\frac{1}{2}$$ turn?

Solution:
Yes, the design looks the same after $$\frac{1}{2}$$ turn.

Does this design looks the same after $$\frac{1}{4}$$ turn?

Solution:
No, the design does not look the same after $$\frac{1}{4}$$ turn.

Colour the square given in the adjoining figure using two colours so that the design looks the same after every $$\frac{1}{4}$$ turn.

How many times does this shape look the. same during a full turn?

Do these designs have reflection symmetry also? Draw the line(s) of symmetry.

Solution:

The image looks the same after every $$\frac{1}{4}$$ turn.

During one complete rotation, the figure appears the same four times. The shaded design does not exhibit reflection symmetry.

NCERT Textbook Pages 139-140

Let Us Do

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.

Solution:
Students should do it by themselves.

Does this shape have reflection symmetry? If yes, draw its line(s) of symmetry.

Solution:

Yes, the shape does have reflection symmetry. The lines of symmetry are shown in the picture below.

Does it have rotational symmetry? If yes, at which turn?

Solution:

The shape has rotational symmetry of $$\frac{1}{2}$$ turn also.

Does it have both symmetries?

Solution:
Yes.

NCERT Textbook Page 140

Let Us Explore

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.

Solution:

NCERT Textbook Page 141

Let Us Do

Observe the shapes given on the border. Which of the shapes have reflection symmetry? Put a mark on them. Put a on the shapes that have rotational symmetry.

The design A looks the same after every $$\frac{1}{4}$$ turn.

The design B looks the same after every ____________ turn. This design has _________________symmetry.

Solution:

Students should do it by themselves.

Project Work

Create symmetrical patterns and designs using vegetable blocks. Some are shown below.

Solution:

Students should do it by themselves.

Understanding Symmetry in Mathematics

Learning about symmetry and designs helps Class 5 students recognize patterns in their daily life. The chapter makes it fun to identify reflection symmetry and rotational symmetry in letters, numbers, and beautiful traditional art.

Exploring the NCERT solutions Class 5 Maths Mela Chapter 10 Symmetrical Designs (2025-26) boosts problem-solving and creative skills. By practicing different questions, students understand how symmetry appears in crafts, block printing, and even in English alphabets.

Tip: Always look for lines of symmetry while drawing or making paper designs. This easy habit can improve exam performance and make working with shapes and patterns fun and rewarding!