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Line & Rotational Symmetry

1

Symmetrical or Not? (Set A)

Sort each shape: does it have line symmetry or not?

Square
Circle
Heart
Star
Moon
Diamond
Has line symmetry
No line symmetry
2

Symmetrical or Not? (Set B)

Sort each item.

Butterfly
Apple
Fish
Triangle (equilateral)
Flower
Feather
Symmetrical
Not symmetrical
3

How Many Lines of Symmetry? (Set A)

Circle the correct number of lines of symmetry.

Square

1
2
4

Rectangle (not square)

1
2
4

Equilateral triangle

1
2
3

Circle

4
8
Infinite
4

How Many Lines of Symmetry? (Set B)

Circle the correct number.

Isosceles triangle

0
1
3

Regular pentagon

3
5
10

Regular hexagon

3
6
12

Scalene triangle

0
1
3
5

Match Shapes to Symmetry Lines

Draw a line from each shape to its number of lines of symmetry.

Square
Equilateral triangle
Regular pentagon
Regular hexagon
3 lines
4 lines
5 lines
6 lines
6

Is This a Line of Symmetry? (Set A)

Circle YES or NO.

A vertical line through the middle of a heart

YES
NO

A diagonal line through a square

YES
NO

A horizontal line through the letter B

YES
NO

A vertical line through the letter A

YES
NO
7

Is This a Line of Symmetry? (Set B)

Circle YES or NO.

A horizontal line through the letter H

YES
NO

A vertical line through the letter S

YES
NO

A vertical line through the letter T

YES
NO

A horizontal line through the letter D

YES
NO
8

Sort Letters: Symmetrical or Not

Sort these capital letters.

A
B
F
H
M
N
O
P
Has line symmetry
No line symmetry
9

True or False? (Symmetry)

Circle TRUE or FALSE.

A circle has infinite lines of symmetry

TRUE
FALSE

The letter Z has line symmetry

TRUE
FALSE

A square has 4 lines of symmetry

TRUE
FALSE

Every shape has at least 1 line of symmetry

TRUE
FALSE
10

Complete the Symmetrical Pattern (Set A)

What comes next to make the pattern symmetrical?

?
?
?
11

Complete the Symmetrical Pattern (Set B)

Fill in the missing shapes.

?
?
?
?
?
12

Draw Lines of Symmetry

Draw all the lines of symmetry on each shape.

Draw lines of symmetry on a square:

Draw here

Draw lines of symmetry on an equilateral triangle:

Draw here

Draw lines of symmetry on a regular hexagon:

Draw here
13

Match Shapes to Symmetry Type

Draw a line to match.

Square
Circle
Parallelogram (not rectangle)
Scalene triangle
Equilateral triangle
No line symmetry
Infinite lines
3 lines
4 lines
No line symmetry
14

Identify Symmetrical Shapes

Circle the symmetrical shape in each group.

Which is symmetrical?

Letter F
Letter A
Letter J

Which is symmetrical?

Letter G
Letter P
Letter M

Which has the MOST lines of symmetry?

Square
Rectangle
Triangle
15

Lines of Symmetry Pairs

The total is the number of lines of symmetry of a regular polygon.

3
3
?
4
?
4
5
5
?
6
?
6
8
8
?
16

Symmetrical or Not? (Set C)

Sort each item: symmetrical or not?

Rectangle
Arrow shape
Letter S
Letter T
Letter Z
Pentagon (regular)
Has line symmetry
No line symmetry
17

Symmetrical or Not? (Set D)

Sort each item.

Cup
Book (closed)
Clock face
Pencil
Spoon
Sun
Symmetrical
Not symmetrical
18

How Many Lines of Symmetry? (Set C)

Circle the correct number.

Regular pentagon

3
5
10

Regular hexagon

3
6
12

Isosceles triangle

0
1
3

Rhombus (not square)

1
2
4
19

How Many Lines of Symmetry? (Set D)

Circle the correct number.

Regular octagon

4
8
16

Right-angled triangle (not isosceles)

0
1
2

Kite

0
1
2

Trapezium (isosceles)

0
1
2
20

Match Shapes to Number of Symmetry Lines

Draw a line from each shape to its number of lines of symmetry.

Circle
Square
Equilateral triangle
Rectangle (not square)
Scalene triangle
0
2
3
4
Infinite
21

Match Letters to Symmetry

Draw a line to match each letter with its symmetry type.

Letter A
Letter B
Letter X
Letter N
Letter O
2 lines of symmetry
1 vertical line
1 horizontal line
No line symmetry
Infinite lines (approximately)
22

Symmetrical Letters (Set A)

Circle the letter that has a vertical line of symmetry.

Which has a vertical line of symmetry?

A
F
G

Which has a horizontal line of symmetry?

B
L
P

Which has BOTH vertical and horizontal symmetry?

X
R
K

Which has NO line of symmetry?

N
M
W
23

Symmetrical Letters (Set B)

Circle the correct answer.

Which has a vertical line of symmetry?

T
J
S

Which has a horizontal line of symmetry?

E
A
T

Which has NO lines of symmetry?

F
V
D

Which has the MOST lines of symmetry?

O
H
I
24

Complete the Symmetrical Pattern (Set C)

Fill in the missing shapes to make the pattern symmetrical.

?
?
?
25

Complete the Symmetrical Pattern (Set D)

Complete the symmetrical pattern.

?
?
?
?
26

Draw Lines of Symmetry (Set B)

Draw all lines of symmetry on each shape.

Draw lines of symmetry on a regular pentagon:

Draw here

Draw lines of symmetry on an isosceles triangle:

Draw here

Draw lines of symmetry on the letter H:

Draw here
27

Draw the Other Half

Draw the other half of each shape to make it symmetrical.

Half of a butterfly (left side given). Draw the right side:

Draw here

Half of a house (left side given). Draw the right side:

Draw here

Half of a star (top half given). Draw the bottom half:

Draw here
28

Identify Symmetrical Shapes (Set B)

Circle the symmetrical shape.

Which is symmetrical?

Letter R
Letter V
Letter Q

Which has the MOST symmetry?

Regular hexagon
Kite
Parallelogram

Which everyday object is symmetrical?

A fork
A scissors (closed)
A pen cap

Which shape has exactly 1 line of symmetry?

Isosceles triangle
Square
Circle
29

Symmetry in Nature

Think about symmetry in the real world.

Name 3 things in nature that have line symmetry:

Name 2 things in your classroom that have line symmetry:

Is a human face perfectly symmetrical? Explain:

30

Sort by Number of Symmetry Lines

Sort each shape into the correct column.

Scalene triangle
Isosceles triangle
Equilateral triangle
Square
Parallelogram
Regular hexagon
0 lines
1 line
2 or more lines
31

Symmetry Lines – Regular Polygons

A regular polygon with N sides has N lines of symmetry. Find the missing value.

3
?
3
4
4
?
5
?
5
6
6
?
8
?
8
10
10
?
32

Rotational Symmetry (Set A)

Does the shape look the same when rotated? Circle YES or NO.

A square rotated 90°

YES — looks the same
NO — looks different

The letter F rotated 90°

YES — looks the same
NO — looks different

A circle rotated any amount

YES — looks the same
NO — looks different

An equilateral triangle rotated 120°

YES — looks the same
NO — looks different
33

Rotational Symmetry (Set B)

Circle YES or NO.

A rectangle rotated 180°

YES — looks the same
NO — looks different

The letter L rotated 90°

YES — looks the same
NO — looks different

A regular hexagon rotated 60°

YES — looks the same
NO — looks different

A star (5 points) rotated 72°

YES — looks the same
NO — looks different
34

Order of Rotational Symmetry

How many times does the shape match itself in one full turn?

Square (rotational symmetry order)

1
2
4

Equilateral triangle (rotational order)

2
3
6

Regular hexagon (rotational order)

3
6
12

Rectangle (rotational order)

1
2
4
35

Draw Symmetrical Patterns (Set A)

Complete each pattern so it is symmetrical across the line of symmetry.

Draw the other half of a butterfly so it is symmetrical:

Draw here

Draw a symmetrical pattern using squares and triangles:

Draw here
36

Draw Symmetrical Patterns (Set B)

Create symmetrical designs.

Draw a shape with exactly 2 lines of symmetry:

Draw here

Draw a shape with exactly 4 lines of symmetry:

Draw here
37

Complete the Symmetrical Shape

Half the shape is given. Draw the other half.

The left half of a symmetrical shape is drawn. Complete the right half:

Draw here

The top half of a symmetrical shape is drawn. Complete the bottom half:

Draw here
38

Symmetry in Words and Numbers

Answer these questions.

List all capital letters that have a vertical line of symmetry:

List all capital letters that have a horizontal line of symmetry:

Which digits (0–9) have line symmetry?

39

Symmetry Reasoning

Answer these thinking questions.

A shape has line symmetry but no rotational symmetry. Give an example.

A shape has rotational symmetry but no line symmetry. Is this possible? Explain.

How are line symmetry and rotational symmetry different?

40

Challenge: Design a Symmetrical Tile

Create a tile design.

Design a symmetrical tile pattern with at least 2 lines of symmetry:

Draw here

Explain the symmetry in your design:

41

Home Activity: Symmetry All Around

Explore symmetry in your environment!

  • 1Fold paper in half, cut a shape, and unfold — you made a symmetrical shape!
  • 2Look at letters of the alphabet. Which ones have line symmetry?
  • 3Find 5 symmetrical objects at home (plates, windows, butterflies in books).
  • 4Use a small mirror on a picture. Can you find the line of symmetry?
42

How Many Lines of Symmetry? (Set A)

Circle the correct number of lines of symmetry.

Square:

2
4
8

Equilateral triangle:

1
3
6

Regular hexagon:

3
6
8

Rectangle (not square):

1
2
4
43

Sort: Has Symmetry or No Symmetry?

Sort each shape or letter into the correct column.

Letter A
Letter S
Letter H
Letter F
Equilateral triangle
Scalene triangle
Circle
Parallelogram (non-rectangle)
Has line symmetry
No line symmetry
44

Match Shape to Number of Lines of Symmetry

Draw a line from each shape to its number of lines of symmetry.

Circle
Square
Regular pentagon
Isosceles triangle
Scalene triangle
0 lines
1 line
5 lines
4 lines
Infinite lines
45

Rotational Symmetry

Find the order of rotational symmetry for each shape.

A square has rotational symmetry of order ___ (it looks the same ___ times in one full rotation).

An equilateral triangle has order ___ rotational symmetry.

A regular hexagon has order ___ rotational symmetry.

A rectangle (not a square) has order ___ rotational symmetry.

46

Drawing Lines of Symmetry

Describe where you would draw lines of symmetry for each shape.

Draw all lines of symmetry for a rectangle. How many are there?

Draw all lines of symmetry for a regular octagon. How many are there?

Does a circle have a finite or infinite number of lines of symmetry? Explain.

47

Completing Symmetric Designs

Describe how to complete each symmetric design.

The left half of a butterfly is drawn. Describe how to complete it using line symmetry.

A design has 4-fold rotational symmetry. One quarter is complete. Describe the other quarters.

48

Symmetry in the Real World

Circle the correct answer.

A stop sign (octagon) has how many lines of symmetry?

4
8
6

A flag with a single stripe down the middle has:

1 line of symmetry
2 lines
No symmetry

The letter Z has what type of symmetry?

Line symmetry
Rotational symmetry order 2
No symmetry

A snowflake typically has:

3-fold symmetry
6-fold symmetry
8-fold symmetry
49

Symmetry and Pattern

Investigate symmetry in patterns.

Create a pattern on a 4×4 grid that has exactly 1 line of symmetry. Describe it.

Does a checkerboard pattern have line symmetry? How many lines?

50

Lines of Symmetry in Letters

Survey capital letters A–Z. Tally how many have each number of lines of symmetry.

ItemTallyTotal
0 lines of symmetry
1 line of symmetry
2 lines of symmetry
More than 2
51

Transformations: Reflections

Describe the reflection of each point across the given line.

Point (3, 2) reflected across the y-axis: new position = ___

Point (4, -1) reflected across the x-axis: new position = ___

A rectangle at (1,1), (4,1), (4,3), (1,3) reflected across x = 5: new coordinates?

52

Transformations: Rotations

Describe what happens when each shape is rotated.

Rotate a square 90° clockwise about its centre. Does it look different? Why/why not?

Rotate the letter F 180° about its centre. What does it look like?

What rotation (quarter, half or three-quarter turn) maps the letter Z onto itself?

53

Transformations: Translations

Describe or perform each translation.

Point (2, 5) is translated 3 right and 4 down. New position: ___

A triangle has vertices (0,0), (3,0), (0,4). Translate it 5 right and 2 up. New vertices: ___

What is the difference between a reflection and a translation?

54

Challenge: Symmetry Investigation

Investigate this symmetry puzzle.

Can a shape have rotational symmetry but no line symmetry? Give an example.

Can a shape have line symmetry but no rotational symmetry (order > 1)? Give an example.

Design a logo that has both line symmetry and rotational symmetry. Describe it.

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