Class 5 Mathematics · Chapter 10

10. Symmetrical Designs

Solutions to all Let Us Do, Let Us Think and Let Us Explore questions. CBSE / NCERT Class 5 Maths Mela.

Alphabet Cutout

1Which of the alphabet cutouts E, N, X, T, K, V, O can be made by just drawing half or quarter of the letter?

By drawing half: E, T, K, V (they have one line of symmetry).

By drawing a quarter: X and O (they have two lines of symmetry).

N cannot be made this way. It has no line of symmetry.

2Which letters have a horizontal line of symmetry? A vertical line of symmetry? Both?

Horizontal line of symmetry: E, K, X, O

Vertical line of symmetry: T, V, X, O

Both vertical and horizontal: X, O

3Let Us Do: Use lines of symmetry to make paper cutouts of diya, boat and other designs.

Activity. Fold the paper along the line of symmetry, draw half the design along the fold, cut and open.

Let Us Make a Windmill Firki

1Observe the dot in the firki. Does the firki look the same after ¼, ½, ¾ and a full turn?

Yes. The firki looks the same after a ¼ turn, ½ turn, ¾ turn and a full turn.

2Observe the letters. Do they look the same when turned?

Letter	¼ turn	½ turn	¾ turn	Full turn	Rotational symmetry
H	No	Yes	No	Yes	Yes, at ½ turn
I	No	Yes	No	Yes	Yes, at ½ turn
X	Yes	Yes	Yes	Yes	Yes, at ¼, ½ and ¾ turn
Y	No	No	No	Yes	No

Every shape looks the same after a full turn. We say a shape has rotational symmetry only if it looks the same before completing a full turn.

Let Us Do — Symmetry in Digits

1Find symmetry in the digits 1 to 9 and 0.

Digits with reflection symmetry: 0, 1, 3, 8

Digits with rotational symmetry: 0, 1, 8 (they look the same after a ½ turn)

Digits with both symmetries: 0, 1, 8

6 and 9 turn into each other after a ½ turn.

2Do the numbers 11 and 1001 have (a) rotational symmetry, (b) reflection symmetry or (c) both?

Both 11 and 1001 have (c) both rotational and reflection symmetries.

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

Type	2-digit	3-digit	4-digit
Rotational only	69	609	6699
Reflection only	33	303	3113
Both	11, 88	101, 808	1001, 8008

Making Designs

(a)Does the design have rotational symmetry?

No. There is a circle only on the right side. After a ½ turn, the circle comes to the left side.

(b)Add shape(s) so that the new design looks the same after a ½ turn.

Add one more circle on the left side, next to the left triangle. Now the design looks the same after a ½ turn.

(c)Modify or add more shapes so that the new design looks the same after a ¼ turn.

Make the top and bottom triangles point outwards, like the left and right triangles. Add circles at the top and bottom also. Now all four arms are the same, so the design looks the same after every ¼ turn.

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

Yes. The design in (b) has 2 lines of symmetry — one vertical and one horizontal.

The design in (c) has 4 lines of symmetry — vertical, horizontal and two slanting (diagonal) lines.

Let Us Think

1Does the green and pink design look the same after a ½ turn? After a ¼ turn?

After a ½ turn: Yes.

After a ¼ turn: No. The green and pink squares change places.

It has 2 lines of symmetry along the two diagonals.

2Colour the square using two colours so that it looks the same after every ¼ turn. How many times does it look the same during a full turn?

Colour the 8 triangles one by one in two colours going around the centre (red, blue, red, blue, …). This makes a pinwheel design.

It looks the same 4 times during a full turn (after ¼, ½, ¾ and full turn).

This pinwheel design has no line of symmetry.

Let Us Do — Squares and Triangles

1Does this shape (4 squares with 2 triangles on each side) have reflection symmetry? Rotational symmetry? Both?

Reflection symmetry: Yes. It has 2 lines of symmetry — one vertical and one horizontal.

Rotational symmetry: Yes, at a ½ turn.

So, it has both symmetries.

2Make your designs and sort them into 3 categories.

Activity. Arrange the squares and triangles in different ways. Check each design for lines of symmetry and for turns. Sort them as: only rotational, only reflection, and both.

Let Us Explore — Block Printing

1Match each wooden block to its correct print.

(i) → (c)
(ii) → (d)
(iii) → (a)
(iv) → (e) (given)
(v) → (b)

2The design B looks the same after every ____ turn. This design has ____ symmetry.

The design B looks the same after every ¼ turn. This design has rotational symmetry. (It also has reflection symmetry.)

Let Us Do

1Observe the shapes on the border. Put a ✓ on shapes with reflection symmetry and a * on shapes with rotational symmetry.

Shapes like the star, hexagon, square, circle, octagon and rhombus have both — mark them ✓ and *.

The triangle, the pentagon and the three-circle shape have reflection symmetry (✓) and also look the same after a ⅓ or ⅕ turn (*).

The tilted rectangle and parallelogram look the same after a ½ turn (*). The pinwheel at the bottom has only rotational symmetry (*).

Project Work

1Create symmetrical patterns and designs using vegetable blocks.

Project. Cut a lady’s finger, potato or onion across. Dip it in colour and print. Repeat the print after equal turns or in mirror positions to make symmetrical designs.

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