Class 5 Mathematics

Chapter 10 Solutions — Symmetrical Designs

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Solutions

Overview

Step-by-step NCERT solutions for Symmetrical Designs (Chapter 10, NCERT Class 5 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Symmetrical Designs textbook chapter.

Solved

What these solutions cover

All 12 questions in Symmetrical Designs are solved in the PDF. Here's what's inside, exercise by exercise:

Alphabet Cutout — Lines of Symmetry in Letters (p. 136)

1.
Which of the following alphabet cutouts can be made by just drawing half (1/2) or quarter (1/4) of the letter? Draw lines of symmetry on the letters to find out. E N X T K V O
- (a) Which of the letters have a horizontal line of symmetry?
- (b) Which of the letters have a vertical line of symmetry?
- (c) Which letters have both vertical and horizontal lines of symmetry?

Let Us Do

Use lines of symmetry to make paper cutouts of a diya, a boat, and other designs. Look along the border of the page to find the pictures.

Let Us Make a Windmill Firki — Rotational Symmetry (p. 137)

Observe the dot in the firki. Does the firki look the same after 1/4, 1/2, 3/4, and a full turn?
Observe the letters H, I, X, and Y in the table. Do they look the same when turned? Complete the table to show which letters have rotational symmetry.

Let Us Do — Symmetry in Digits 0–9 (p. 138)

1.
Find symmetry in the digits 1 2 3 4 5 6 7 8 9 0.
- (a) Which digit(s) have reflection symmetry?
- (b) Which digit(s) have rotational symmetry?
- (c) Which digit(s) have both rotational and reflection symmetries? Now look at the numbers: || and |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…

Making Designs — Rotational and Reflection Symmetry (p. 139)

1.
Look at the design (a large blue cross shape with triangles and circles). Answer the following:
- (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 a 1/4 turn. Draw…

Let Us Think — Colouring for Rotational Symmetry (p. 139)

Look at the shape below: a 2x2 blue square with a triangle attached on its left side and another on its right side, both pointing outward. 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?

Let Us Do — Symmetrical Designs with Squares and Triangles (p. 139–140)

1.
Cut out squares and equilateral triangles with the same side length (provided at the end of the book). Make different symmetrical designs by using these two shapes. For the sample design shown (two triangles flanking a 2x2 arrangement of blue squares, with triangles on opposite sides):
- (a) Does this shape have reflection symmetry? If yes, draw its line(s) of symmetry.
- (b) Does it have rotational…

Let Us Explore — Block Printing and Symmetry (p. 140–141)

1.
Match each wooden block to its correct print by drawing a line. One is done for you (block iv is matched to print e). Blocks:
- (i) large paisley/mango-leaf shape,
- (ii) lotus flower,
- (iii) large floral mandala,
- (iv) half-circle fan [matched to
- (e) already],
- (v) thin vertical leaf/vine Prints:
- (a) round floral rosette,
- (b) thin green leaf vine,
- (c) paisley/mango-leaf half,
- (d) yellow lotus,
- (e) red…
2.
Observe the pattern made by a leaf-shaped wooden block printed 4 times to make a cross-like design (Design A). Design A looks the same after every 1/4 turn. Now look at Design B (a four-petal flower shape with dashed lines).
- (a) The design B looks the same after every ___ turn.
- (b) This design has ___ symmetry.

Let Us Do — Border Shapes: Reflection and Rotational Symmetry (p. 141)

Observe the shapes given on the border of the page. Which of the shapes have reflection symmetry? Put a tick (v) mark on them. Put a * on the shapes that have rotational symmetry.

Project Work — Symmetrical Patterns with Vegetable Blocks (p. 141)

1.
Create symmetrical patterns and designs using vegetable blocks. Two examples are shown:
- (a) an okra (bhindi) cross-section stamped to make a flower pattern, and
- (b) a potato cut to make oval prints arranged in a 3x3 grid with two colours.

Sample

Worked examples

A question from Symmetrical Designs, solved step by step.

Let Us Make a Windmill Firki — Rotational Symmetry (p. 137)

Observe the dot in the firki. Does the firki look the same after 1/4, 1/2, 3/4, and a full turn?

A firki (windmill) has 4 blades arranged equally around the centre.

When you turn it by 1/4 turn (90 degrees), one blade moves to where the next blade was — the firki looks exactly the same.

This is true for every 1/4 turn: after 1/4, 2/4 (= 1/2), 3/4, and a full (4/4) turn, the firki looks the same.

The dot on the blade helps you track how far it has turned, but the overall shape (all 4 blades) looks identical at each of these positions.

So: Yes, the firki looks the same after 1/4 turn, 1/2 turn, 3/4 turn, and a full turn.

Answer: Yes. The firki looks the same after every 1/4 turn (at 1/4, 1/2, 3/4, and full turn) because it has 4 equal blades.

All 12 questions in Symmetrical Designs are solved step by step in the Solutions PDF above.

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Chapter 10 Solutions — Symmetrical Designs

Overview

What these solutions cover

Alphabet Cutout — Lines of Symmetry in Letters (p. 136)

Let Us Do

Let Us Make a Windmill Firki — Rotational Symmetry (p. 137)

Let Us Do — Symmetry in Digits 0–9 (p. 138)

Making Designs — Rotational and Reflection Symmetry (p. 139)

Let Us Think — Colouring for Rotational Symmetry (p. 139)

Let Us Do — Symmetrical Designs with Squares and Triangles (p. 139–140)

Let Us Explore — Block Printing and Symmetry (p. 140–141)

Let Us Do — Border Shapes: Reflection and Rotational Symmetry (p. 141)

Project Work — Symmetrical Patterns with Vegetable Blocks (p. 141)

Worked examples

Observe the dot in the firki. Does the firki look the same after 1/4, 1/2, 3/4, and a full turn?

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