NCERT Solutions Class 5 Maths Chapter 10 Symmetrical Designs

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 5 · M AT H S

NCERT Solutions

Chapter 10: Symmetrical Designs

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

136 – 141 13 38 English

Solutions, notes, sample papers & more at 64 pages

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 10: Symmetrical Designs
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).

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 136 – 141

SECTIONS QUESTIONS

13 38

MEDIUM

English

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

ALPHABET CUTOUT

Q1 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.

You only have to draw half of the A. The fold makes the other half for you.
First look at the letter A. It has one line of symmetry — a line standing straight up through the
middle. A line of symmetry is a folding line. Fold along it and the two halves sit exactly on each
other.

Page 1 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Step 1 Step 2 Step 3 Step 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.

Do it like this:

1. Fold a paper in half. Press the fold flat so you can see it clearly.
2. Draw half of the letter A along the fold. Keep the tip of the A on the fold. Draw only one
slanting leg and half of the crossbar.
3. Cut along the outline. Cut through both layers of the paper together. Do not cut the fold
itself.
4. Open the paper. The full letter A is ready.

Why it happens: When the paper is folded, the two layers lie exactly on each other.
Whatever you cut on the top layer is cut the same way on the bottom layer. So the
second half comes out as the mirror image of the first half — and that is exactly
what a line of symmetry means.

Check it yourself: Open your cut-out A and fold it back along the same line. The two
halves should cover each other with nothing sticking out. If they do, your A is
symmetrical.

Q2 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.

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.

Page 2 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The two lines of H are: one standing up (vertical) and one lying flat (horizontal). Fold along both
and the paper becomes one-fourth of its size.

Step 1 Step 2 Step 3 Step 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.

Do it like this:

1. Fold the paper into one-fourth. Fold it once up-and-down, then fold it once side-to-side.
Now the paper has two folded edges.
2. Draw one-fourth of the letter H along the folds. It looks like a small letter L touching both
folded edges.
3. Cut along the outline. Cut all four layers together.
4. Open the paper. The full letter H is ready.

Why it happens: The first fold copies your drawing once. The second fold copies it
again. One drawing → two copies → four copies. That is why one-fourth of the letter
is enough.

Tip: This only works when the letter really has two lines of symmetry. Try it with the
letter G and you will get a strange shape, because G has no line of symmetry at all.

Q3 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

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.

Page 3 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

The rule is short:
co m
se m.
m a
The letter has one line of symmetry → draw half the letter on one fold.
The letter c o l
.has two lines of symmetry → draw one-fourth of the letteragon two folds.
The s m
e has no line of symmetry → you must draw the whole letter.
l a letter
ag

co m
e m . ag
E N X T K V O a g l as

half whole quarter half half half
com
quarter
m .
m as e
. co a g l
Red dashed lines are the lines of symmetry.
e m
g l as
a
N has no dashed line, so N has to be drawn fully. X and O have two lines each.

m a s
m .co agl
se
E → 1 line (flat) → draw half

g l a
a
N → 0 lines → draw the whole letter

X → 2 lines → draw a quarter

co m
T → 1 line (upright) → draw half
m .
m as e
.co
K → 1 line (flat) → draw half
a g l
a s eVm→ 1 line (upright) → draw half
agl
m
O → 2 lines → draw a quarter

a se
. com a g l
m
ase
agl
Why N is different: N does look the same when you turn it half a turn, but turning is
not folding. There is no line along which N folds onto itself. So the folding trick fails
for N.

co m
m .
m as e
.co a g l
a s emQ4 Which of the letters have a horizontal line of symmetry? _________________

agl
.c
s e m
com gl a
E, K, X and O.
m . a
A horizontal line of symmetry s
a e flat, straight across the letter. Fold the letter along it and the
l
lies
agon the bottom half.
top half must land exactly

co m
m .
m ase
.co


a g l Page 4 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

E K X O
Top half folds down onto the bottom half.

E, K, X and O each fold neatly along a flat line.

Why: In E, the top arm and the bottom arm are the same, and the middle arm sits
on the fold. In K, the upper slanting arm and the lower slanting arm are the same. In
X the four arms are alike. O is a smooth oval, the same above and below.

Watch out: T and V do not have a flat folding line. Fold T across the middle and the
crossbar has nothing to land on.

Q5 Which of the letters have a vertical line of symmetry? ____________________

T, V, X and O.
A vertical line of symmetry stands straight up. Fold the letter along it and the left half must land
exactly on the right half.

Page 5 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

T V X O
Left half folds across onto the right half.

T, V, X and O each fold neatly along an upright line.

Why: T has a crossbar the same length on both sides and a stem right in the middle.
V has two slanting arms that mirror each other. X and O are the same on the left and
on the right.

Did you notice? The letter A also has a vertical line of symmetry — that is how Prem
cut it at the start of the chapter. A is just not in this list of seven letters.

Q6 Which letters have both vertical and horizontal lines of symmetry? ________

X and O.
These two letters pass both folding tests.

1. Fold side to side. X folds onto itself. O folds onto itself.
2. Fold top to bottom. X folds onto itself again. O folds onto itself again.
3. So each of them has two lines of symmetry.

Page 6 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

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

Try This: Fold a paper into one-fourth and draw just a quarter of the letter O — a
small curve. Cut and open it. A perfect O comes out.

Why it matters: More lines of symmetry means less drawing. One line → draw half.
Two lines → draw a quarter. That is the whole idea of the Alphabet Cutout activity.

Let Us Do — Page 136

Page 7 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Paper cutouts of the pictures printed on the border

LET US DO

Q1 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.

diya boat leaf tree butterfly

four-leaf
heart kite umbrella flower clover

arrow circle bow

Pictures printed along the border of page 136.

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.
Look along the border. You will find a diya (lamp), a boat, a leaf, a tree, a butterfly, a heart, a
kite, an umbrella, a flower, a four-leaf clover, an arrow, a circle and a bow.
Method — do it step by step:

1. Choose a picture from the border, say the diya.
2. Find its folding line. For all these pictures the line stands straight up through the middle.
3. Fold a paper in half and press the fold flat.
4. Draw only the half picture that lies on one side of the line, keeping its straight edge on the
fold.
5. Cut along the outline through both layers. Do not cut the fold.
6. Open the paper. The full diya appears.

Page 8 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
Opened out —sae full m.
om a
Half
e m . cdrawn on the fold diya agl
s
a gla

co m
e m . ag
g l as
a

co m
e m.
. co las
m dashed line is the fold = the line of symmetry.
The
ag
e m
g l as Half a diya on the fold becomes a whole diya when you open the paper.
a
m a s
.co agl
Sample answer: I folded a sheet in half. On the fold I drew half a boat — a slanting

a s em
side, the flat bottom and half of the sail. I cut along the outline and opened it. The

agl exactly the same. I did the same for the diya, the leaf,
boat came out with both sides
the butterfly and the heart, and pasted them on a chart.

com
m .
o m l a se
Why the fold is the trick: When the paper is folded, the two layers sit exactly on
.c other. One cut makes two matching halves at the same
a g time. So you never have
m
aseto make the second half match — the fold does it for you.
each

agl
se m
com g l a
Let Us Make a Windmill Firkiem
. a
— Page 137
a s
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
em . co agl
g l as
a

com
m .
m ase
.co


a g l Page 9 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Lali's firki, and what happens when you turn it

LET US MAKE A WINDMILL FIRKI

Q1 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.

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.

1. Take a square paper. A square is needed so that all four blades come out the same size.
2. Fold it corner to corner. You get two triangles. Open it out.
3. Fold it corner to corner the other way. You get two more triangles. Open it out.
4. Look at the paper. The two folds cross in the middle and make an X. The point where they
cross is the centre.
5. Cut along the four lines of the X — but stop about halfway to the centre. Do not cut all the
way, or the paper will fall into four pieces.
6. Take one corner of each cut triangle and bend it gently to the centre. Hold it there. Do not
press the fold flat, or the blade will not catch the wind.
7. Do this for every other corner — one corner from each of the four blades, going the same
way round.
8. Push a pin through the four folded corners and through the centre of the paper.
9. Push the pin into a stick or straw. Your firki is ready.

The X made by Cut only halfway in The finished firki
two folds

Page 10 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Two diagonal folds, four half-cuts, four corners pinned to the centre.

Why the corners go to the centre: Each folded corner makes a slanting blade.
Wind pushing on a slanting blade pushes it sideways, and that side-push turns the
firki round the pin.

Tip: Always fold the same corner of every blade — all four to the left, or all four to
the right. If you mix them, the blades push against each other and the firki will not
spin.

Q2 Make sure the pin is not too tight. Check if your windmill spins when the wind is
blowing.

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

1. Test the pin first. Flick one blade with your finger. The firki should go round several times on
its own.
2. If it stops at once, the pin is too tight. Pull it back a little so the paper can turn against the
stick.
3. If it wobbles and falls off, the pin is too loose. Push it in a little more.
4. Now take it outside, or hold it in front of a fan, and watch it spin.

Why the pin must be loose: The paper has to turn while the stick stays still. If the
pin squeezes the paper against the stick, the two are locked together and nothing
can turn.

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.

Q3 Observe the dot in the firki. Does the firki look the same after 1/4, 1/2, 3/4, and a
full turn? ___________________.

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

Page 11 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The green dot is only there to help you see that the firki really has moved. The dot travels round,
but the firki itself looks unchanged.

Initial position 1/4 turn 1/2 turn 3/4 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.

The firki has 4 blades, all the same, spaced equally.

One full turn shared among 4 blades = 1 ÷ 4 = 1/4 turn

So it looks the same at 1/4, 1/2, 3/4 and full turn — 4 times in one full turn

Why it happens: After a 1/4 turn, blade 1 sits exactly where blade 2 was, blade 2
where blade 3 was, and so on. All the blades look alike, so you cannot tell that
anything moved. This is called rotational symmetry.

Remember the book's line: "A firki has rotational symmetry, as it looks the same
when rotated by 1/4, 1/2 and 3/4 turn."

Turning the Letters — Page 138

Page 12 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The table of letters H, I, X and Y at 1/4, 1/2, 3/4 and full turn

LET US DO

Q1 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. (Complete the table for H, I, X
and Y.)

ORIGINAL 1⁄ 1⁄ 3⁄ FULL ROTATIONAL
4 TURN 2 TURN 4 TURN
LETTER TURN 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.

Here is the completed table. H, I and X all have rotational symmetry at a 1/2 turn. Y has none.

Page 13 of 64

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Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

m
.co
ORIGINAL 1/4 TURN 1/2 TURN 3/4 FULL ROTATIONAL

se m
com a
LETTER TURN TURN SYMMETRY

. ag l
(YES/NO)

H as
em
agl
lying down, looks the same lying looks the Yes, at 1/2 turn
like ⌶ —H down same — H
turned again

. com ag
e m lying flat
as
I (a straight bar) lying flat, looks the same looks the Yes, at 1/2 turn
like — —I
a g l again same — I

X like a + looks the same like a + looks the Yes, at 1/2 turn

co m
m.
—X same — X

m as e
.co l
arms point upside down, arms
g
Y looks the No

a
sem
left arms at the point same — Y

a
agl
bottom right

How to test a letter — do it yourself:
m a s
em
.co
1. Cut the letter out of paper, or copy it on tracing paper.
agl
a s
l and compare it with the printed letter.
2. Fix its centre with a pin or a nail. The red dot in the book marks this centre.

aground
3. Turn it a quarter of the way
4. Keep turning — half, three-quarters, full. Note down each time it matches.

co m
.
5. If it matches before the full turn is over, the letter has rotational symmetry.

se m
o m l a
g but it has really
m .c the white dots are drawn: The letter may look the same
Why
a
asemoved. The small white dots ride round with the letter and tell you how far it has
agl turned. The shape matching is what counts, not the dot.

se m
com g l a
m . a
e
as same after a 1/4 turn, 1/2 turn, 3/4 turn and a full turn?
Letter I — does it look lthe
Q2
a g
Does it have rotational symmetry (Yes/No)?

co m
m .
e

c o m g l as
.
Yes — the letter I has rotational symmetry, at a 1/2 turn. It does not look the same after a
a
sem
1/4 turn or a 3/4 turn.
a
agl c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 14 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

start 1/4 turn 1/2 turn 3/4 turn full
different same different same

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

Why: The letter I is just a straight bar. Its top end and its bottom end look exactly
alike. So turning it upside down changes nothing you can see.

Q3 Letter 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)?

Yes — the letter X has rotational symmetry, at a 1/2 turn. After a 1/4 turn it becomes a plus
sign, which is not the same as X.

start 1/4 turn 1/2 turn 3/4 turn full
different same different same

A quarter turn makes X stand up as a plus sign. A half turn brings the X back.

Page 15 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

1/4 turn → looks like + → different

1/2 turn → looks like X → same

3/4 turn → looks like + → different
Full turn → same

Rotational symmetry: Yes, at 1/2 turn

Why not at 1/4 turn? The four arms of X are equally spaced, but they are spaced a
half turn apart in pairs. Turning by a quarter turn puts an arm where there was
empty space, so the letter now leans a different way.

Did you know? X is the only letter in this table that also has lines of symmetry — an
upright one and a flat one. So X has both reflection symmetry and rotational
symmetry.

Q4 Letter 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)?

No — the letter Y has no rotational symmetry. It matches the start only after a full turn, and
a full turn does not count.

start 1/4 turn 1/2 turn 3/4 turn full
different different different same

The two arms of Y point up at the start. After every part-turn they point somewhere else.

Page 16 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

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

Why: Y has two arms at the top and one long stem at the bottom. The top and the
bottom are not alike. So no part-turn can make it look the same.

But Y is not without symmetry: Y has a vertical line of symmetry. Fold it down the
middle and the left arm lands on the right arm. So Y has reflection symmetry but no
rotational symmetry.

Let Us Do — Find symmetry in the digits — Page 138
1 2 3 4 5 6 7 8 9 0, and the numbers 11 and 1001

LET US DO

Q1 Find symmetry in the digits. 1 2 3 4 5 6 7 8 9 0 — Which digit(s) have reflection
symmetry? ___________________________

0, 1, 3 and 8.
Test each digit the way you tested the letters: draw a line on it and fold. Use the shapes exactly
as they are printed in your book — there the digit 1 is a plain straight bar, with no flag and no
foot.

3 8 0 2
1 — both lines 3 — flat line 8 — both lines 0 — both lines 2 — no line

Red dashed lines are lines of symmetry.

Page 17 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The digit 2 is shown for comparison — no fold works on it.

DIGIT LINE OF SYMMETRY? WHICH LINE

0 Yes upright and flat

1 (a bar) Yes upright and flat

2 No —

3 Yes flat (horizontal)

4 No —

5 No —

6 No —

7 No —

8 Yes upright and flat

9 No —

Why 3 has only a flat line: The top curve of 3 and the bottom curve of 3 are the
same. Fold it across and they land on each other. But the left side of 3 is open while
the right side is round, so an upright fold does not work.

Check it yourself: Hold a small mirror upright, touching the flat line of a 3. Look into
it. You see a 3 again. Now hold the mirror upright along the middle of a 3 — you get
a strange shape, not a 3.

Q2 Which digit(s) have rotational symmetry? ___________________________

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

Page 18 of 64

ase
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

m
m .co
before the turn
m l a se
after a 1/2 turn
. co ag
e m 0 8
8 0
g l as →
a

co m
em . ag
s
gla down. They read the same.
Turn the page upside
a
1, 8 and 0 are unchanged when the paper is turned upside down.
co m
em.
m l as
.co a g
a s em
1 upside down → 1 ✓

agl 8 upside down → 8 ✓
m a s
agl
0 upside down → 0 ✓

6 upside down → 9 ✗ (it changes intom . c o
a s e a different digit)

9 upside down → 6 ✗ agl

co m
m .
Why 6 and 9 do not count: Rotational symmetry means the shape must look like
m as e
.co a g l
itself again. A 6 turned half way round becomes a 9. That is a different digit, so 6 has

s e m rotational symmetry on its own.
no

agla
se m
a
Try This: Write 1, 8 and 0 boldly on a card. Turn the card upside down and hold it up.
om you turned it.
Your friends will not be able to tellcthat
. a g l
a s em
agl
Q3 Which digit(s) have both rotational and reflection symmetries? ________
co m
m .
m as e
.co
a g l
a s em0, 1 and 8.
agl 1. Digits with a line of symmetry: 0, 1, 3, 8.
.c
s e m
m a
agl
2. Digits with rotational symmetry: 0, 1, 8.
. co
m
3. Take the ones in both lists: 0, 1 and 8.

as e
a g l

co m
m .
m ase
.co


a g l Page 19 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Reflection: {0, 1, 3, 8}

Rotational: {0, 1, 8}

Both: {0, 1, 8}
Only reflection: 3

Neither: 2, 4, 5, 6, 7, 9

Why 3 is left out: 3 folds neatly along a flat line, so it has reflection symmetry. But
turn a 3 upside down and you get a shape like a backwards E — not a 3. So it has no
rotational symmetry.

Did you know? There is no digit here with rotational symmetry but no line of
symmetry. Among the letters, though, N is exactly like that.

Q4 Now, let us look at the following numbers: 11 , 1001. Do these have (a) rotational
symmetry, (b) reflection symmetry or (c) both symmetries?

(c) Both symmetries. Both 11 and 1001 have reflection symmetry and rotational symmetry.
Remember, in the book each 1 is a plain bar and each 0 is a smooth oval.

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.

Test 1 — the folding test (reflection):

1. Fold 11 down the middle, between the two bars. The left bar lands on the right bar. ✓
2. Fold 11 across the middle. Each bar folds onto itself. ✓

Page 20 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

3. Fold 1001 down the middle, between the two zeros. The left 1 lands on the right 1, the left 0
on the right 0. ✓
4. Fold 1001 across the middle. Every digit folds onto itself. ✓

Test 2 — the turning test (rotational):

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 ✓

Why the flipping does not spoil it: A half turn reverses the order of the digits. In
1001 the order reversed is 1‑0‑0‑1 — the very same number. Numbers that read the
same forwards and backwards are called palindromes, and that is why 1001 survives
the turn.

Q5 Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry,
reflection symmetry, or both.

Here are examples of each kind. First remember which digits can be used.

For a flat (horizontal) line of symmetry, use only 0, 1, 3, 8. Each of these folds across on its
own, and the order of digits stays as it is.
For an upright (vertical) line of symmetry, use only 0, 1, 8, and the number must read the
same backwards.
For a 1/2 turn, use 0, 1, 8 (which stay the same) and the pair 6, 9 (which swap), and the
number must still read the same after the order is reversed.

HOW MANY REFLECTION SYMMETRY ROTATIONAL BOTH
DIGITS SYMMETRY

2-digit 13, 30, 38 (flat line); 11, 88 (upright 69, 96, 11, 88 11, 88
line)

3-digit 318, 803 (flat line); 101, 181, 808 619, 916, 101, 111, 808 101, 181, 808,
(upright line) 888

4-digit 3018, 8130 (flat line); 1001, 1881, 8008 6009, 1691, 1001, 8118 1001, 1881,
(upright line) 8008, 8118

Check two of them:

Page 21 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

69 turned a half turn: 6 → 9 and 9 → 6, and the order flips

So 69 → 69 ✓ rotational symmetry

318 folded along a flat line: 3 → 3, 1 → 1, 8 → 8, order unchanged

So 318 → 318 ✓ reflection symmetry (flat line)

Why the order flips for turning but not for folding across: A half turn moves the
number end over end, so the last digit arrives first. Folding along a flat line only flips
each digit up and down; the digits stay in their places.

Try This: Write 1691 on a slip of paper and turn it upside down. It still says 1691.
Now try 1961 — it becomes 1961 too? Check carefully and you will see it does not.
Only some arrangements work.

Making Designs — Page 139

Page 22 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The 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.

No. The design does not have rotational symmetry.
Look at the design carefully first. It is made of a circle in the middle, four triangles round it, and
one more small circle on the right.

Page 23 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
em.
m l as
m .co a g
l a se
a g

co m
em . ag
g l as
a

co m
e m.
m l as
m .co a g
l a se
ag
The design as printed in the book
om a s
Notice: the left triangle points inwards, m
e
. c agl
s
the right one points outwards, and there is only one small
a circle — on the right.
agl
om
Test it, step by step:

1. Try a 1/4 turn. The top triangle would move to the right side. But the m
. c
s e right side already has a

.
triangle la not match.
compointing the other way, and a small circle beyond it. Itagdoes
a s em
l
2. Try a 1/2 turn. The small circle on the right would move to the left. There is nothing on the

ag left for it to land on. It does not match.
3. Try a 3/4 turn. Again nothing matches.
se m
com g l a
.
4. Only a full turn brings the design back — and a full turn does not count.
m a
ase
1/4 turn → does not match agl
m
1/2 turn → does not match
. co
e m
as
3/4 turn → does not match
m l
m.coFull turn → matches, but this is true for every shape
a g
l a se
ag So: no rotational symmetry

.c
s e m
co m gl a
. a
Why: For rotational symmetry, every piece must have a partner waiting for it in the
m
new place. Here the lone s
a e circle on the right has no partner anywhere. One odd
l
small
ag the symmetry.
piece is enough to spoil

co m
m .
m as e
.co


a g l Page 24 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

But it is not symmetry-free: Fold the design along a flat line through the middle.
The top triangle lands on the bottom triangle, and the side pieces fold onto
themselves. So this design does have reflection symmetry — one horizontal line of
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.

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.

Page 25 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Looks the same after a 1/2 turn
The red dot is the centre. Turn the picture upside down — it looks exactly the same.

How to build it, step by step:

1. Copy the design into your notebook.
2. Mark the centre — the middle of the big circle.
3. Look at each piece and ask: what is directly opposite it, on the other side of the centre?
4. Top triangle ↔ bottom triangle. Already a pair. ✓
5. Left triangle points inwards, but the right one points outwards. Turn the right triangle
round so it also points inwards. Now they are a pair. ✓
6. The small circle on the right has nothing opposite it. Add a small circle on the left, the
same size and the same distance away. ✓
7. Now check: turn the notebook upside down. The design looks unchanged.

Pairs after the change:

top triangle ↔ bottom triangle

left triangle ↔ right triangle

left small circle ↔ right small circle

big circle ↔ itself (it sits on the centre)

Page 26 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The rule for a 1/2-turn design: Every piece must have a twin standing straight
across the centre, at the same distance, turned the other way. If even one piece is
alone, the half turn will show it.

Another correct answer: Instead of turning the right triangle, you may add a
triangle at each side so that both sides become bow-tie shapes, and add the left
circle. Any design where each piece has an opposite twin is right.

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.

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.

Page 27 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Looks the same after every 1/4 turn
Four identical arms, spaced equally round the centre.

How to build it, step by step:

1. Draw the big circle in the middle of your page and mark its centre.
2. Draw one arm — a triangle pointing outwards with a small circle at its tip.
3. Copy that arm exactly to the right of the centre.
4. Copy it again below the centre, and once more to the left.
5. All four arms must be the same size and the same distance from the centre.
6. Turn your notebook a quarter of the way round. Each arm sits where the next one was, so
the design looks unchanged.

Page 28 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
e m.
Number of equal arms = 4
m l as
.co
One full turn ÷ 4 = 1/4 turn
m a g
l a se
g
So it looks the same at 1/4, 1/2, 3/4 and full turn = 4 times in a full turn
a

. com
Why 4 equal arms give a 1/4 turn: A quarter turn moves arm 1 to where arm 2 was,
ag
a s em 4 to arm 1. Since all four look alike, you
arm 2 to arm 3, arm 3 to arm 4 and arm
cannot see any change.
agl

co m
m.
Notice: A design that looks the same after a 1/4 turn also looks the same after a 1/2

m as e
.co l
turn (two quarter turns together). So this design answers part (b) as well.
a g
se m
g l a
a
(d) Do the new designs have reflection symmetry? If yes, draw the lines of
s
Q4
m a
.co agl
symmetry.

se m
g l a
a

Yes — both new designs have reflection symmetry. The 1/2-turn design has 2 lines of
symmetry. The 1/4-turn design has 4.
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
a s em Design (b): 2 lines of symmetry Design (c): 4 lines of symmetry

agl
Red dashed lines are the folding lines. Fold along any of them and the two halves match.
.c
s e m
m a
Design (b) — check each line:
e m . co agl
g l as
a
1. Upright line through the centre. The left triangle folds onto the right triangle, and the left
circle onto the right circle. ✓

co m
m .
m ase
.co


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Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

2. Flat line through the centre. The top triangle folds onto the bottom triangle. ✓
3. So design (b) has 2 lines of symmetry.

Design (c) — check each line:

1. Upright line: left arm folds onto right arm. ✓
2. Flat line: top arm folds onto bottom arm. ✓
3. Slanting line one way: top arm folds onto right arm, left arm onto bottom arm. ✓
4. Slanting line the other way: top arm folds onto left arm, right arm onto bottom arm. ✓
5. So design (c) has 4 lines of symmetry.

Why design (c) has more lines: All four arms are exactly alike, so a fold in any of the
four directions still lands an arm on an arm. In design (b) the up-down pair and the
left-right pair are different from each other, so only two folds work.

Important: Rotational symmetry and reflection symmetry do not always come
together. A design can look the same after a 1/4 turn and still have no folding line at
all — you will see one such design in the next activity.

Let Us Think — Page 139

Page 30 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The green-and-pink square, and colouring a square for a 1/4 turn

LET US THINK

Q1 Does this design look the same after 1/2 turn? __________

The design: four small squares — two green and two pink — placed corner to corner.

Yes. The design looks exactly the same after a 1/2 turn.
The design is a big square cut into four small squares. Green sits at the top-left and at the
bottom-right. Pink sits at the top-right and at the bottom-left.

Page 31 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

→
1/2 turn

before after — exactly the
same

A half turn swaps opposite corners, and opposite corners have the same colour.

Top-left (green) goes to bottom-right, which is green ✓

Top-right (pink) goes to bottom-left, which is pink ✓

Bottom-left (pink) goes to top-right, which is pink ✓

Bottom-right (green) goes to top-left, which is green ✓

So the design looks the same after a 1/2 turn

Why it happens: A half turn always sends a corner square to the square diagonally
opposite. Here the diagonal pairs are green–green and pink–pink. Same colour
meets same colour, so nothing appears to change.

Page 32 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Q2 Does the design look the same after 1/4 turn? __________

The design: four small squares — two green and two pink — placed corner to corner.

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

Page 33 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
em.
m l as
m .co a g
l a se
a g
→m
. co ag
m
e1/4 turn
g l as
a
before com
after — the colours
.
m sem
have swapped
a
e m . co agl
g l as
a Green has moved to where pink was, so this is not the same picture.

m a s
m .co agl
a se
A 1/4 turn sends the top-left square to the top-right place.
l
Top-left is green. Top-right was pink. ag
Green now sits where pink used to be → the design has changed
co m
m .
o m l a se
m .c A quarter turn sends each square to the square nextatog it, not the one opposite.
aseNeighbouring squares here have different colours, so the change shows at once.
Why:

agl
se m
com g l a
.
Remember: A design can look the same after a 1/2 turn but not after a 1/4 turn. The
m a
ase
1/2 turn is the easier test to pass.

agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

com
m .
m ase
.co


a g l Page 34 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Q3 Colour 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.

Colour the eight triangles turn by turn — orange, blue, orange, blue — all the way round.
That is the only way to do it with two colours.
The square in the book is already divided by dashed lines: both diagonals and both middle lines.
That makes 8 equal triangles round the centre.

Page 35 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

the empty squarecoloured
(8 turn by turn — a pinwheel
Turntriangles)
it a quarter of the way round: orange still lands
on orange.

Eight triangles, coloured alternately. This makes a pinwheel pattern.

How to colour it, step by step:

1. Count the triangles. The dashed lines make 8 equal triangles round the centre.
2. Start anywhere and colour that triangle orange.
3. Colour the next one round blue.
4. Keep going round — orange, blue, orange, blue — until all 8 are coloured.
5. You will have 4 orange triangles and 4 blue triangles, sitting in a pinwheel pattern.

Why this works: A 1/4 turn moves each triangle two places round the ring. Counting
round the ring, place 1 goes to place 3, place 2 to place 4, and so on. If you colour
turn by turn, place 1 and place 3 are the same colour, place 2 and place 4 are the
same colour — so every triangle lands on its own colour.

Check it yourself: Trace your coloured square on tracing paper. Put a pin at the
centre and turn the tracing a quarter of the way round. The colours should sit
exactly on top of the ones below.

Page 36 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Q4 How 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.

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

Full turn = 1

It looks the same after every 1/4 turn

How many quarter turns in a full turn? 1 ÷ 1/4 = 4

So it looks the same 4 times in one full turn

Page 37 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

1/4 turn 1/2 turn 3/4 turn full turn

The same picture appears four times while the square goes once round.

Why it is 4 and not 8: There are 8 triangles, but they are of two colours. A shift of
one triangle would put orange on blue. Only a shift of two triangles — that is a
quarter turn — keeps the colours right. Four such shifts make one full turn.

Tip for any design: Count how many equal, identical parts go round the centre. That
number is how many times the design looks the same in one full turn.

Page 38 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
m.
Do these designs have reflection symmetry also? Draw the line(s) of symmetry.
e
Q5

m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
ag

co m
m .
m as e
.co a g l
se m
g l a
a
se m
co—mtwo green and two pink — placed corner to corner. g l a
. a
em
The design: four small squares

a s
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 39 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The square printed in the book. The dashed lines — both diagonals and both middle
lines — divide it into eight equal triangles round the centre.

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.

Page 40 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

2 lines of symmetry no line of symmetry
Turning symmetry and folding symmetry are two
different things.

The pinwheel turns beautifully but never folds onto itself.

The green-and-pink square — test each fold:

1. Fold side to side. Green (top-left) lands on pink (top-right). ✗
2. Fold top to bottom. Green lands on pink again. ✗
3. Fold along the slanting line from top-left to bottom-right. Green stays on green, and the
two pink squares swap. ✓
4. Fold along the other slanting line. Pink stays on pink, and the two green squares swap. ✓
5. So it has 2 lines of symmetry — the two diagonals.

The pinwheel square — test each fold:

1. Fold side to side, top to bottom, or along either diagonal.
2. Every time, an orange triangle lands on a blue triangle. ✗
3. So the pinwheel has no line of symmetry.

Why the pinwheel cannot fold: The colours go round in one direction — orange,
blue, orange, blue. A fold reverses the direction, so the order becomes blue, orange,
blue, orange. That is the opposite of what is printed, and it never matches.

Big idea: The pinwheel has rotational symmetry but no reflection symmetry. The
letter V has reflection symmetry but no rotational symmetry. The letter X and design
(c) have both. All four kinds are possible.

Page 41 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

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

LET US DO

Q1 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.

Squares and equilateral triangles with the same side length — the cut-outs given at the
end of the book.

Arrange the shapes evenly round one centre point. If every arm of your design is the same,
the design will be symmetrical.
Take the cut-outs from the sheets at the end of the book. Both shapes have the same side
length, so any side of a square fits exactly along any side of a triangle.

Page 42 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

A star: 1/4-turn and 4 lines A lamp shape: 1/2-turn and 2 lines
of symmetry of symmetry

Two designs made from one square and some triangles.

How to make a symmetrical design:

1. Put one square in the middle of your page.
2. Stick one triangle on the top edge of the square, pointing outwards.
3. Do the same on the right edge, the bottom edge and the left edge. You now have a four-
pointed star.
4. Test it by turning. Turn the page a quarter of the way round — the star looks the same.
5. Test it by folding. Fold it side to side, top to bottom, and along both slanting lines — all four
folds match.
6. Now change it — put triangles on only the top and bottom edges. This new design looks the
same after a 1/2 turn and folds along 2 lines.

Sample answer: I made three designs. 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: four squares in a row with
one triangle at each end — it has 1 line of symmetry and looks the same after a 1/2
turn.

The rule you are practising: Put the same thing at every arm and the design will
have rotational symmetry. Make the two sides of every arm alike and it will have
lines of symmetry as well.

Page 43 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
m.
Symmetry in a Shape — Page 140
m as e
.co
Four blue squares with a triangle on each side
a g l
a s em
aQ1gl Does this shape have reflection symmetry? If yes, draw its line(s) of symmetry.

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
em
.co agl
a s
l square on the left and on the right.
The shape: four blue squares joined in a block, with a cream triangle on the outer edge

aofgeach

co m
m .
o m l a se
m .c shape has 2 lines of symmetry — one upright and oneagflat, both passing through the
se
Yes. This

g l amiddle.
a First see what the shape is made of: four blue squares joined in a block, with a cream triangle on

se m
com a
the outer edge of each square on the left and on the right.

. a g l
m
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
em . co agl
g l as
a

com
m .
m ase
.co


a g l Page 44 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Two lines of symmetry, drawn in red
Fold along either red line and the two halves cover each other exactly.

Test each fold:

1. Fold along the upright line (between the left squares and the right squares). The two left
triangles land on the two right triangles. The two left squares land on the two right squares.
✓
2. Fold along the flat line (between the top squares and the bottom squares). The upper
triangle on each side lands on the lower triangle on that side. ✓
3. Try a slanting fold. A triangle would have to land on the top edge of the block, where there
is no triangle. ✗

Upright fold → works ✓

Flat fold → works ✓

Slanting folds → do not work ✗

Number of lines of symmetry = 2

Why the slanting fold fails: There are triangles on the left and the right, but none
on the top or the bottom. A slanting fold tries to send a left triangle up to the top,
and there is nothing there to match it.

Page 45 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Q2 Does 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.

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.

Page 46 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

1/4 turn → the side triangles would move to the top and bottom → does not match

1/2 turn → left triangles go to the right, right triangles go to the left → matches ✓

3/4 turn → does not match

So: rotational symmetry at a 1/2 turn, and the shape looks the same 2 times in a full turn

Why: The shape is built the same way on the left and on the right. A half turn simply
swaps those two sides, and since they are alike, nothing looks different. A quarter
turn would move them to the top and bottom, where the shape is plain.

Q3 Does 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.

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

KIND OF DOES THE SHAPE HAVE DETAILS
SYMMETRY IT?

Reflection symmetry Yes 2 lines — one upright, one flat

Rotational symmetry Yes at a 1/2 turn; looks the same 2 times in a full
turn

Page 47 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Why the two go together here: Folding along the upright line and then along the
flat line has the same effect as turning the shape half way round. So once a shape
has two lines of symmetry crossing at right angles, it must also look the same after a
half turn.

Check it yourself: Trace the shape. Fold your tracing side to side, open it, then fold
it top to bottom. Now instead, turn the tracing half way round. You end up with the
same picture both ways.

Q4 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.

Make several designs, then test each one twice — once by folding and once by turning —
and put it in the right group.
How to sort a design:

1. Fold test. Try folding it side to side, top to bottom, and along the slanting lines. If any fold
matches, the design has reflection symmetry.
2. Turn test. Trace it, pin the centre and turn. If it matches before a full turn is over, the design
has rotational symmetry.
3. Put it in a group using the two answers.

only rotational only reflection both

One example for each of the three groups.

The pinwheel only turns; the isosceles triangle only folds; the square does both.

Page 48 of 64

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Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
m.
Sample answer:

m l a se
Only rotational symmetry: my pinwheel square from the Let Us Think activity; a
o
design of.3c leaves all curving the same way round a centre. ag
e m
sreflection
g l
Onlya symmetry: a triangle with a square below it, like a small house; a
abutterfly cut-out.
Both: a square with a triangle on each of its four sides; the four-blue-squares shape
co m
above; a plain circle.
e m . ag
g l as
a
What makes the difference: If every arm of your design curls the same way round
the centre, you get turning symmetry but no folding line — folding would reverse
co m
the curl. If your arms are straight and evenly placed, you get both kinds.
em.
m l as
m .co a g
l a se
g
a Us Explore — Block Printing — Page 140
Let

m a s
m .co agl
l a se
ag

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


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Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Matching the wooden blocks of Rajasthan to their prints

LET US EXPLORE

Q1 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 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).

Page 50 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

The matches are: (i)–(c), (ii)–(d), (iii)–(a), (iv)–(e) (already done for you) and (v)–(b).
Each print in the lower row shows only half of the block's design — the half on one side of its
line of symmetry. So to match them, look at the half and imagine the fold.

BLOCK WHAT THE BLOCK SHOWS PRINT WHAT THE PRINT SHOWS

(i) a mango-shaped paisley (buta) with a ring (c) half a paisley with the same
of small scallops all round scalloped edge

(ii) a lotus with pointed petals and a leaf (d) half a pointed lotus with half a leaf
below below

(iii) a round flower (rosette) with petals all (a) half a round flower
round

(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 (b) half a plant — the stem and the
leaves on both sides leaves on one side only

How to match them yourself:

1. Look at the outline of the print. Is it round, pointed, tall and thin, or a fan?
2. Find the block with the same outline. A tall thin print must come from the tall thin block.
3. Check the small details. Count the scallops on the edge, or look at the shape of the petals.
4. Imagine the fold. Hold a mirror on the straight edge of the print. The picture you see
should look like the whole block.

→

the printed half the whole block design
A mirror on the dashed line turns half a design into the whole design.

Page 51 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Why the prints show only half: The carved block is symmetrical, so half of it already
tells you everything. Block printers use this: the two halves of the pattern always
match, which is what makes the printed cloth look neat.

Did you know? Block printing (thappa chhapai) is a traditional craft of Rajasthan.
Artisans carve a design into a wooden block, dip it in colour and press it on cloth,
again and again. The craft has been practised for centuries and makes Rajasthan's
textiles special.

The Print Made by One Block — Page 141

Page 52 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Design A (the leaf cross) and design B (the four hearts)

Q1 Observe 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 block Print

A

The wooden block carries one leaf. Print A is what you get when the block is used four
times.

One leaf block, stamped four times — pointing up, right, down and left — makes the
whole design A.
Look at the wooden block: it carries just one leaf. Now look at the print: there are four leaves,
arranged like a plus sign.

Page 53 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m.co a g
l a se
a g
→ co m
m . ag
se
stamp 4 times
a
agl
m
m .co
the block — one
se
design A — four leaves
a
comleaf
. ag l
m
ase
agl Between one stamp and the next, the block is turned a quarter of the way round.

m a s
em
.co agl
s
How the print is made:
a
agl up.
1. Stamp once with the leaf pointing
2. Turn the block a 1/4 turn and stamp again — the leaf now points right.

co m
.
3. Turn another 1/4 turn and stamp — the leaf points down.

e m
as
4. Turn once more and stamp — the leaf points left.
m l
.co
5. Four stamps, and design A is complete.
m a g
l a se
ag Number of leaves = 4, all alike, evenly placed

se m
One full turn ÷ 4 = 1/4 turn
com g l a
m. a
ase
So design A looks the same after every 1/4 turn

agl
It looks the same 4 times in one full turn

. c om
s
Why the print has the symmetry: The block itself was turnede mby a quarter turn
a
om stamps. Whatever movement you use to makeagalpattern
.cbetween
m movement that leaves it unchanged.
becomes the

l a se
ag
.c
s e m
m a
agl
Design A also folds. Each leaf is the same on its left and right. So design A has 4
. co
m
lines of symmetry as well — upright, flat, and the two slanting ones.
as e
a g l

co m
m .
m ase
.co


a g l Page 54 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Q2 The 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.

The design B looks the same after every 1/4 turn. This design has both rotational and
reflection symmetry.
Design B is made of four heart-shaped petals, one pointing up, one right, one down and one
left, all meeting at the centre.

Page 55 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Design B, with its two lines of
symmetry

The dashed lines are the ones printed in your book. Fold along either and the halves match.

Reasoning, step by step:

1. Count the petals. There are 4, all exactly alike.
2. Share the full turn among them. 1 full turn ÷ 4 = a 1/4 turn.
3. Turn the page a quarter of the way round. Each petal sits where the next one was, so the
design looks unchanged. That is rotational symmetry.
4. Now fold it. The book has already drawn the two folding lines — one upright, one flat. Fold
along either and the two halves cover each other. That is reflection symmetry.

Page 56 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

5. So design B has both kinds of symmetry.

Looks the same after: 1/4 turn, 1/2 turn, 3/4 turn, full turn

Number of times in a full turn = 4
Lines of symmetry = 2 (upright and flat)

Why it is like design A: Both designs were made in the same way — one carved
shape, stamped four times, turned a quarter turn each time. Same method, same
symmetry.

Let Us Do — Shapes on the border — Page 141

Page 57 of 64

Class 5 Maths Chapter 10 Symmetrical Designs AglaSem · NCERT Solutions

Tick the shapes with reflection symmetry, star the ones with rotational symmetry

LET US DO

Q1 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 shapes printed along the border of page 141.

Almost every shape on the border gets a tick, and most of them get a star too. Two shapes
are the exceptions — the orange slanting four-sided shape and the thin red triangle.
Use one simple rule for the regular shapes:

A regular shape with n equal sides has:

n lines of symmetry (so it gets a ✓)

and it looks the same after a 1/n turn (so it gets a *)

Page 58 of 64

as e
Class 5 Maths Chapter 10 Symmetrical Designs
a g l AglaSem · NCERT Solutions

m
.co
SHAPE ON THE REFLECTION ROTATIONAL HOW MUCH OF A
TURN m
se
✓
com a
BORDER SYMMETRY ( ) SYMMETRY (*)

. l
ag1/4 turn
m
ase
Light blue square (left side) ✓ 4 lines *

gl green circle (left side)
aLight ✓ many lines * any turn at all

m
.co
✓ 3 lines
ag
Purple triangle (left side) * 1/3 turn

a sem
agl
Yellow hexagon, 6 sides ✓ 6 lines * 1/6 turn
(top)

Green six-pointed star (top) ✓ 6 lines *
co
1/6 turn
m
e m.
m as
✓ 3 lines
.co l
Pink triangle split into 4 * 1/3 turn

a g
m
small triangles (top)

l a se
g
a with cut corners (top)
Grey-and-green triangle ✓ 3 lines * 1/3 turn

m * a s
.co agl
Three purple circles joined ✓ 3 lines 1/3 turn

se m
a
by a Y (top)

a g l
Red rectangle (right side) ✓ 2 lines * 1/2 turn

✓ 2 lines (its diagonals)
co m
.
Grey rhombus, a slanted * 1/2 turn
diamond (right side)
se m
om 5 sides l a
Olive.cpentagon,
m ✓ 5 lines ag 1/5 turn
ase(right side)
*

agl Green heptagon, 7 sides ✓ 7 lines * 1/7 turn
se m
(right side)
com g l a
m . a
ase
✓
agl
Purple star-ring of triangles * it looks the same at
(right side) each small turn round
the ring

✓ 2 lines . c1/2omturn
m
Mauve bow-tie of two *

m as e
l
triangles (left side)

.co a g
a s em overlapping stars (bottom
Yellow and grey ✓ 3 lines * 1/3 turn

agl
left)
.c
s e m
m a
.co agl
Pink triangle with a circle at ✓ 3 lines * 1/3 turn
each corner (bottom)
a s em
Blue four-blade cross agl✓ 4 lines * 1/4 turn
(bottom right)

com
m .
m ase
.co


a g l Page 59 of 64