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NCERT Solutions for Class 5 Maths Chapter 10 Symmetrical Designs (PDF) – 2027

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NCERT Solutions for Class 5 Maths Chapter 10 Symmetrical Designs – step-by-step answers to every exercise and in-text question of the chapter, as per the latest NCERT syllabus for 2027. Read them online or download the free question-answer PDF.

Chapter 10 of Math Mela is about symmetrical designs — pictures that stay the same when you fold them or when you turn them. Prem and Manu cut letters for a birthday wall, Lali makes a paper firki that spins, and block printers of Rajasthan stamp one small wooden block again and again. From these you learn two ideas: reflection symmetry (a folding line, called a line of symmetry) and rotational symmetry (the shape looks the same after a part-turn).

NCERT Solutions for Class 5 Maths Chapter 10 Symmetrical Designs PDF

All the answers are on this page below. The PDF also explains every answer – why it is right and how to check it – so download it for revision.

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NCERT Solutions for Class 5 Maths Chapter 10 Symmetrical Designs – Questions and Answers

All 38 questions of the chapter (textbook pages 136 – 141) are answered below, in the order of the book – in-text questions, activities and the end-of-chapter exercises. Each answer is written the way you would write it in the exam.

Alphabet Cutout — Page 136Prem and Manu cut letters for Lali’s birthday wall

Alphabet Cutout
Q1The 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.
Answer

You only have to draw half of the A. The fold makes the other half for you.

Step 1Step 2Step 3Step 4 The red dashed line is the fold — the line of symmetry of A.
Fold, draw half, cut, open. The fold line becomes the middle of the letter A.
Q2The 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.
Answer

For H you draw only one-fourth of the letter. H has two lines of symmetry, so two folds do the rest of the work.

Step 1Step 2Step 3Step 4 Two red dashed lines = the two lines of symmetry of H.
One-fourth of H looks like a small L. Two folds turn that L into a full H.
Q3Which 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
ENXTKVO
The letters printed in the book: E, N, X, T, K, V, O.
Answer

Half (1/2) is enough for E, T, K, V, X and O. Quarter (1/4) is enough for X and O. N cannot be made this way — it has no line of symmetry.

ENX TKV O halfwholequarter halfhalfhalfquarter Red dashed lines are the lines of symmetry.
N has no dashed line, so N has to be drawn fully. X and O have two lines each.
Q4Which of the letters have a horizontal line of symmetry? _________________
ENXTKVO
The letters printed in the book: E, N, X, T, K, V, O.
Answer

E, K, X and O.

EKXO Top half folds down onto the bottom half.
E, K, X and O each fold neatly along a flat line.
Q5Which of the letters have a vertical line of symmetry? ____________________
ENXTKVO
The letters printed in the book: E, N, X, T, K, V, O.
Answer

T, V, X and O.

TVXO Left half folds across onto the right half.
T, V, X and O each fold neatly along an upright line.
Q6Which letters have both vertical and horizontal lines of symmetry? ________
ENXTKVO
The letters printed in the book: E, N, X, T, K, V, O.
Answer

X and O.

XO Two folding lines each
Because they have two lines of symmetry, one-fourth of the letter is enough to cut them.

Let Us Do — Page 136Paper cutouts of the pictures printed on the border

Let Us Do
Q1Use lines of symmetry to make paper cutouts of diya, boat, and other designs. Look along the border of the page to find the pictures.
diyaboatleaftreebutterflyheartkiteumbrellaflowerfour-petalflowerarrowcirclebowclubpaper plane
Pictures printed along the border of page 136.
Answer

Fold the paper once, draw only half the picture along the fold, cut, and open. Every picture on the border of page 136 has one folding line.

Half drawn on the fold Opened out — a fulldiya The dashed line is the fold = the line of symmetry.
Half a diya on the fold becomes a whole diya when you open the paper.

Let Us Make a Windmill Firki — Page 137Lali’s firki, and what happens when you turn it

Let Us Make a Windmill Firki
Q1Lali 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.
Answer

You need a square paper, scissors, a pin and a stick or straw. Work slowly at step 5 — that is where most firkis go wrong.

The X made bytwo folds Cut onlyhalfway in The finishedfirki
Two diagonal folds, four half-cuts, four corners pinned to the centre.
Q2Make sure the pin is not too tight. Check if your windmill spins when the wind is blowing.
Answer

Hold the firki up in the breeze, or run with it. If the pin is loose enough, it spins freely.

Sample answer: My firki did not spin at first. I loosened the pin a little and blew on it. Then it spun easily. In the school ground the wind made it spin without my blowing at all.
Q3Observe the dot in the firki. Does the firki look the same after 1/4, 1/2, 3/4, and a full turn? ___________________.
Initial position1/4 turn1/2 turn3/4 turnFull turn
The firki in its starting position and after each quarter turn. The green dot shows how far it has turned.
Answer

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

Initial position1/4 turn1/2 turn3/4 turn The green dot moves. The firki does not change.
The blades sit in the same four places every quarter turn, so the firki looks unchanged.

Turning the Letters — Page 138The table of letters H, I, X and Y at 1/4, 1/2, 3/4 and full turn

Let Us Do
Q1Observe 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. (Complete the table for H, I, X and Y.)
Original letter1⁄4 turn1⁄2 turn3⁄4 turnFull turnRotational symmetry (Yes/No)
Yes, at 1⁄2 turn
     
     
     
The table from the book. The red dot marks the centre the letter is turned about; the small white dots ride round with the letter so you can see where it has got to. The row for H is already filled in.
Answer

Here is the completed table. H and I look the same after a 1/2 turn. X looks the same after every 1/4 turn. Y has no rotational symmetry.

Original letter1/4 turn1/2 turn3/4 turnFull turnRotational symmetry (Yes/No)
Hon its side — not the samelooks the same — Hon its side again — not the samelooks the same — HYes, at 1/2 turn
I (a straight bar)lying flat — not the samelooks the same — Ilying flat again — not the samelooks the same — IYes, at 1/2 turn
Xlooks the same — Xlooks the same — Xlooks the same — Xlooks the same — XYes, at 1/4, 1/2 and 3/4 turn
Yarms point sideways — not the sameupside down — not the samearms point the other way — not the samelooks the same — YNo
Q2Letter I — does it look the same after a 1/4 turn, 1/2 turn, 3/4 turn and a full turn? Does it have rotational symmetry (Yes/No)?
Answer

Yes — the letter I has rotational symmetry, at a 1/2 turn.

start1/4 turn1/2 turn3/4 turnfull differentsamedifferentsame
Standing up, lying flat, standing up, lying flat. Only the upright ones match the start.
1/4 turn → the bar lies flat → different
1/2 turn → the bar stands up again → same
3/4 turn → the bar lies flat → different
Full turn → back to the start → same
Rotational symmetry: Yes, at 1/2 turn
Q3Letter X — does it look the same after a 1/4 turn, 1/2 turn, 3/4 turn and a full turn? Does it have rotational symmetry (Yes/No)?
Answer

Yes — the letter X has rotational symmetry. It looks the same after a 1/4 turn, a 1/2 turn and a 3/4 turn.

start1/4 turn1/2 turn3/4 turnfull samesamesamesame
After every quarter turn the X looks the same. Only the white dots show that it has moved.
1/4 turn → looks like X → same
1/2 turn → same
3/4 turn → same
Full turn → same
Rotational symmetry: Yes, at 1/4, 1/2 and 3/4 turn (4 times in a full turn, like the firki)
Q4Letter Y — does it look the same after a 1/4 turn, 1/2 turn, 3/4 turn and a full turn? Does it have rotational symmetry (Yes/No)?
Answer

No — the letter Y has no rotational symmetry.

start1/4 turn1/2 turn3/4 turnfull differentdifferentdifferentsame
The two arms of Y point up at the start. After every part-turn they point somewhere else.
1/4 turn → arms point sideways → different
1/2 turn → arms point down → different
3/4 turn → arms point the other way → different
Full turn → back to the start → same
Rotational symmetry: No

Let Us Do — Find symmetry in the digits — Page 1381 2 3 4 5 6 7 8 9 0, and the numbers 11 and 1001

Let Us Do
Q1Find symmetry in the digits. 1 2 3 4 5 6 7 8 9 0 — Which digit(s) have reflection symmetry? ___________________________
Answer

0, 1, 3 and 8.

DigitLine of symmetry?Which line
0Yesupright and flat
1 (a bar)Yesupright and flat
2No—
3Yesflat (horizontal)
4No—
5No—
6No—
7No—
8Yesupright and flat
9No—
Q2Which digit(s) have rotational symmetry? ___________________________
Answer

0, 1 and 8 — each of them looks the same after a 1/2 turn.

before the turnafter a 1/2 turn 80 8 0 → Turn the page upside down. They read the same.
1, 8 and 0 are unchanged when the paper is turned upside down.
1 upside down → 1 ✓
8 upside down → 8 ✓
0 upside down → 0 ✓
6 upside down → 9 ✗ (it changes into a different digit)
9 upside down → 6 ✗
Q3Which digit(s) have both rotational and reflection symmetries? ________
Answer

0, 1 and 8.

Reflection: {0, 1, 3, 8}
Rotational: {0, 1, 8}
Both: {0, 1, 8}
Only reflection: 3
Neither: 2, 4, 5, 6, 7, 9
Q4Now, let us look at the following numbers: 11 , 1001. Do these have (a) rotational symmetry, (b) reflection symmetry or (c) both symmetries?
Answer

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

11 1001 Each number folds along an upright line and along a flat line.
Both numbers read the same in a mirror and the same upside down.
Turn 11 by a half turn → the bars stay bars → reads 11 ✓
Turn 1001 by a half turn → 1 stays 1, 0 stays 0, and the order flips → reads 1001 ✓
Q5Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry, reflection symmetry, or both.
Answer

Here are examples of each kind.

How many digitsReflection symmetryRotational symmetryBoth
2-digit13, 30, 38 (flat line); 11, 88 (upright line)69, 96, 11, 8811, 88
3-digit318, 803 (flat line); 101, 181, 808 (upright line)619, 916, 101, 111, 808101, 181, 808, 888
4-digit3018, 8130 (flat line); 1001, 1881, 8008 (upright line)6009, 1691, 1001, 81181001, 1881, 8008, 8118

Making Designs — Page 139The blue design of triangles and circles

Making Designs
Q1(a) Does the design have rotational symmetry? Yes/No.
The design given on page 139, made of circles and triangles.
Answer

No. The design does not have rotational symmetry.

1/4 turn → does not match
1/2 turn → does not match
3/4 turn → does not match
Full turn → matches, but this is true for every shape
So: no rotational symmetry
Q2(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.
The design given on page 139, made of circles and triangles.
Answer

Add one small circle on the left, and turn the right triangle round so that it points inwards like the left one. Then every piece has a partner exactly opposite it.

Looks the same after a 1/2 turn
The red dot is the centre. Turn the picture upside down — it looks exactly the same.
Q3(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.
The design given on page 139, made of circles and triangles.
Answer

Make all four arms exactly alike: a triangle pointing outwards at the top, right, bottom and left, and a small circle at the end of each arm.

Looks the same after every 1/4 turn
Four identical arms, spaced equally round the centre.
Q4(d) Do the new designs have reflection symmetry? If yes, draw the lines of symmetry.
Answer

Yes — both new designs have reflection symmetry. The 1/2-turn design has 2 lines of symmetry. The 1/4-turn design has 4.

Design (b): 2 lines of symmetry Design (c): 4 lines of symmetry
Red dashed lines are the folding lines. Fold along any of them and the two halves match.

Let Us Think — Page 139The green-and-pink square, and colouring a square for a 1/4 turn

Let Us Think
Q1Does this design look the same after 1/2 turn? __________
The design: four small squares — two green and two pink — placed corner to corner.
Answer

Yes. The design looks exactly the same after a 1/2 turn.

before → 1/2 turn after — exactly thesame
A half turn swaps opposite corners, and opposite corners have the same colour.
Q2Does the design look the same after 1/4 turn? __________
The design: four small squares — two green and two pink — placed corner to corner.
Answer

No. After a 1/4 turn the colours swap places, so the design looks different.

before → 1/4 turn after — the colourshave swapped
Green has moved to where pink was, so this is not the same picture.
Q3Colour the square given in the adjoining figure using two colours so that the design looks the same after every 1/4 turn.
The square printed in the book. The dashed lines — both diagonals and both middle lines — divide it into eight equal triangles round the centre.
Answer

Colour the eight triangles turn by turn — orange, blue, orange, blue — all the way round. Colouring whole triangles, this is the only way to do it with two colours.

the empty square(8 triangles) coloured turn by turn— a pinwheel Turn it a quarter of the way round: orange still landson orange.
Eight triangles, coloured alternately. This makes a pinwheel pattern.
Q4How many times does this shape look the same during a full turn?
The square printed in the book. The dashed lines — both diagonals and both middle lines — divide it into eight equal triangles round the centre.
Answer

4 times — at the 1/4 turn, the 1/2 turn, the 3/4 turn and the full turn.

It looks the same after every 1/4 turn
4 quarter turns make 1 full turn
So it looks the same 4 times in one full turn
1/4 turn1/2 turn3/4 turnfull turn
The same picture appears four times while the square goes once round.
Q5Do these designs have reflection symmetry also? Draw the line(s) of symmetry.
The design: four small squares — two green and two pink — placed corner to corner.
The square printed in the book. The dashed lines — both diagonals and both middle lines — divide it into eight equal triangles round the centre.
Answer

The green-and-pink square: yes — it has 2 lines of symmetry, both slanting (the two diagonals). The pinwheel square you coloured: no — it has no line of symmetry at all.

2 lines of symmetry no line of symmetry Turning symmetry and folding symmetry are twodifferent things.
The pinwheel turns beautifully but never folds onto itself.

Let Us Do — Page 139Making designs from squares and equilateral triangles

Let Us Do
Q1Cut 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.
Squares and equilateral triangles with the same side length — the cut-outs given at the end of the book.
Answer

Arrange the shapes evenly round one centre point.

A star: 1/4 turn,4 lines of symmetry A lamp shape: 1/2 turn,2 lines of symmetry
Two designs made from one square and some triangles.
Sample answer: Design 1: a square with a triangle on each of its four sides — it looks the same after every 1/4 turn and has 4 lines of symmetry. Design 2: a square with triangles only on the top and bottom — it looks the same after a 1/2 turn and has 2 lines of symmetry. Design 3: a square with one triangle on its top edge only — it has 1 line of symmetry but no rotational symmetry.

Symmetry in a Shape — Page 140Four blue squares with a triangle on each side

Q1Does this shape have reflection symmetry? If yes, draw its line(s) of symmetry.
The shape: four blue squares joined in a block, with a cream triangle on the outer edge of each square on the left and on the right.
Answer

Yes. This shape has 2 lines of symmetry — one upright and one flat, both passing through the middle.

Two lines of symmetry, drawn in red
Fold along either red line and the two halves cover each other exactly.
Q2Does it have rotational symmetry? If yes, at which turn?
The shape: four blue squares joined in a block, with a cream triangle on the outer edge of each square on the left and on the right.
Answer

Yes — at a 1/2 turn. It does not look the same after a 1/4 turn.

→ 1/2 turn After a half turn the picture is unchanged.
The left pair of triangles swaps with the right pair, and the block of squares stays a block.
Q3Does it have both symmetries?
The shape: four blue squares joined in a block, with a cream triangle on the outer edge of each square on the left and on the right.
Answer

Yes. This shape has both reflection symmetry and rotational symmetry.

Kind of symmetryDoes the shape have it?Details
Reflection symmetryYes2 lines — one upright, one flat
Rotational symmetryYesat a 1/2 turn; looks the same 2 times in a full turn
Q4Now, 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.
Answer

Make several designs, then test each one twice — once by folding and once by turning — and put it in the right group.

Sample answer:
Only rotational symmetry: my pinwheel square from the Let Us Think activity; a design of 3 leaves all curving the same way round a centre.
Only reflection symmetry: a triangle with a square below it, like a small house; a butterfly cut-out.
Both: a square with a triangle on each of its four sides; the four-blue-squares shape above; a plain circle.

Let Us Explore — Block Printing — Page 140Matching the wooden blocks of Rajasthan to their prints

Let Us Explore
Q1Below 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 blocks
(i)(ii)(iii)(iv)(v)
Prints
(a)(b)(c)(d)(e)
The five wooden blocks and the five prints of page 140, redrawn here in simple outline from the photographs. Each print shows only one half of a block’s design. One match is already made for you: block (iv) goes with print (e).
Answer

The matches are: (i)–(c), (ii)–(d), (iii)–(a), (iv)–(e) (already done for you) and (v)–(b).

BlockWhat the block showsPrintWhat the print shows
(i)a mango-shaped paisley (buta) with a ring of small scallops all round(c)half a paisley with the same scalloped edge
(ii)a lotus with pointed petals and a leaf below(d)half a pointed lotus with half a leaf below
(iii)a round flower (rosette) with petals all round(a)half a round flower
(iv)a half-circle fan with a small knob below(e)a quarter fan with half the knob — done for you
(v)a tall plant with a straight stem and leaves on both sides(b)half a plant — the stem and the leaves on one side only

The Print Made by One Block — Page 141Design A (the leaf cross) and design B (the four hearts)

Q1Observe the pattern made by the wooden block below. We get the final print by using the block 4 times. The design A looks the same after every 1/4 turn.
Wooden blockPrintA
The wooden block carries one leaf. Print A is what you get when the block is used four times.
Answer

One leaf block, stamped four times — pointing up, right, down and left — makes the whole design A.

the block — oneleaf → stamp 4 times design A — four leaves
Between one stamp and the next, the block is turned a quarter of the way round.
Q2The design B looks the same after every ____________ turn. This design has _________________ symmetry.
B
Design B, with the two dashed lines that are printed in the book.
Answer

The design B looks the same after every 1/4 turn. This design has rotational symmetry. It has reflection symmetry too: it folds along the two dashed lines, and along the two slanting lines through the centre.

Design B: 4 lines of symmetry
The upright and flat lines are printed in your book; the two slanting lines work too. Fold along any of them and the halves match.

Let Us Do — Shapes on the border — Page 141Tick the shapes with reflection symmetry, star the ones with rotational symmetry

Let Us Do
Q1Observe 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 shapes printed along the border of page 141.
Answer

Every shape gets a ✓ except the orange parallelogram and the thin red triangle. Every shape gets a * except the thin red triangle.

Shape on the borderReflection symmetry (✓)Rotational symmetry (*)How much of a turn
Light blue square (left side)✓ 4 lines*1/4 turn
Light green circle (left side)✓ many lines*any turn at all
Purple triangle (left side)✓ 3 lines*1/3 turn
Yellow hexagon, 6 sides (top)✓ 6 lines*1/6 turn
Green six-pointed star (top)✓ 6 lines*1/6 turn
Pink triangle made of 3 small triangles, empty in the middle (top)✓ 3 lines*1/3 turn
Grey-and-green triangle with cut corners (top)✓ 3 lines*1/3 turn
Three purple circles joined by a Y (top)✓ 3 lines*1/3 turn
Red rectangle (right side)✓ 2 lines*1/2 turn
Grey rhombus, a slanted diamond (right side)✓ 2 lines (its diagonals)*1/2 turn
Olive pentagon, 5 sides (right side)✓ 5 lines*1/5 turn
Green heptagon, 7 sides (right side)✓ 7 lines*1/7 turn
Purple ring of 10 small triangles (right side)✓ 5 lines*1/5 turn (the small triangles sit in 5 matching pairs)
Mauve bow-tie of two triangles (left side)✓ 2 lines*1/2 turn
Yellow triangle over a grey triangle — a six-pointed star (bottom left)✓ 3 lines*1/3 turn
Pink triangle with a circle at each corner (bottom)✓ 3 lines*1/3 turn
Blue four-blade cross (bottom right)✓ 4 lines*1/4 turn
Orange parallelogram (bottom)no ✓*1/2 turn
Thin red triangle with three unequal sides (left side)no ✓no *only a full turn

Project Work — Page 141Symmetrical patterns with vegetable blocks

Project Work
Q1Create symmetrical patterns and designs using vegetable blocks. Some are shown below.
(a)
(b)
(a) A lady’s finger, its cut face — a small star-like shape — and the flowers printed with it. (b) Potatoes cut in half, and the striped prints made with them.
Answer

Cut a vegetable across, dip the cut face in colour, and press it on paper again and again to build a pattern.

bhindi cut across → four prints, each turned 1/4 This pattern looks the same after every 1/4 turn.
One vegetable block, printed again and again, builds a symmetrical design.
Sample answer: I cut a lady’s finger across and printed its star-like face four times round the centre of my sheet — above, right, below and left — turning it a quarter turn each time. The pattern looks the same after every 1/4 turn. Then I carved a leaf on half a potato and printed a border of leaves round the sheet.

Chapter 10 of 15 – Maths

Also for This Chapter

NCERT Solutions Class 5 Maths Chapter 10 Symmetrical Designs – Overview

ClassClass 5
SubjectMaths
Chapter10 – Symmetrical Designs
Textbook pages136 – 141
Questions solved38
Session2027
FormatFull answers on this page + PDF

NCERT Solutions Class 5 Maths Chapter 10 – FAQs

Where can I download NCERT Solutions Class 5 Maths Chapter 10 Symmetrical Designs PDF?

Read every answer on this page, or download the free PDF from the table at the top.

Is this for the 2027 session?

Yes, it follows the latest NCERT Class 5 Maths book for 2027.

How many questions are solved in NCERT Class 5 Maths Chapter 10?

All 38 questions of the chapter (textbook pages 136 – 141) – the in-text questions, activities and the end-of-chapter exercises.

How should I use these solutions?

Read the chapter in the NCERT book first, attempt the questions yourself, then check your answers here.

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