Symmetry
Lines of Symmetry
Definition :-
A shape has a line of symmetry if, when folded over the line
“the 2 halves of the shape match up exactly”.
Some shapes have more than one line of symmetry :–
1 line of
symmetry
Exercise 1
1.
5 lines of
symmetry
2 lines of
symmetry
(You will need a ruler and tracing paper).
Copy each of the following neatly, using tracing paper.
Mark with a coloured pencil (or a dotted line) all the lines of symmetry.
a
b
c
d
e
f
g
i
j
m
National 4 Book N4-2
h
l
k
n
this is page 36
o
Chapter 3 - Symmetry
2.
In this question, only half of each figure is shown.
Shown also is a line of symmetry (red dotted line).
Copy these shapes into your jotter or onto tracing paper and neatly draw the other half.
3.
a
b
c
d
e
f
Shown below are all the CAPITAL letters of the alphabet.
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z
a
List ALL the letters which have exactly 1 line of symmetry.
b
List ALL the letters which have exactly 2 lines of symmetry.
c
Which letters have NO lines of symmetry ?
d
If the letters
and
are drawn this way,
how many lines of symmetry will each one have ?
National 4 Book N4-2
this is page 37
Chapter 3 - Symmetry
4.
The following shapes have a sloping line of symmetry.
Trace each one onto tracing paper (harder to complete) or copy each one onto
1 centimetre squared paper or trace each one carefully into your jotter
( 12 cm squared) and neatly complete each one.
a
5.
b
c
Do the same here.
This time, each shape has 2 lines of symmetry.
b
a
d
National 4 Book N4-2
e
c
f
this is page 38
Chapter 3 - Symmetry
Half Turn Symmetry
Can you see that this “S” shape has no lines of symmetry ?
It has a different type of symmetry.
centre
•
It has “ 12 –turn symmetry”.
If a pin was stuck in its centre point and the
shape turned (or rotated) by 180° around the
point, it would fit back on itself.
1
2
– turn
(180°)
Exercise 2
1.
Which of the following shapes have
1
2 –turn
symmetry ?
(You might like to use a piece of tracing paper to try them out if you are unsure).
(Do NOT mark the figures in the book).
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
National 4 Book N4-2
this is page 39
Chapter 3 - Symmetry
2.
In Ex 1, you were asked to say which letters of the alphabet had lines of symmetry.
A B C .....
(Look back three pages ).
a
Which seven letters of the alphabet have
b
Of the seven letters which have
1
2 –turn
1
2 –turn
symmetry ?
symmetry, only three do not have a line
of symmetry. Which three ?
1
A shape has “ 2 –turn symmetry” if it only takes a
1
2 –turn
for the shape to fit on itself.
Some shapes have different types of “turn” symmetry.
1
4
•
1
4
•
1
3
– turn symmetry
1
– turn
1
3
•
– turn
– turn symmetry
1
1
6
1
6
– turn symmetry
1
(only needs a 4 turn (90°)
(only needs a 3 turn (120°)
(only needs a 6 turn (60°)
to turn on itself).
to turn on itself).
to turn on itself).
3.
– turn
Say what kind of “turn” symmetry each of the following shapes have.
1
(2 ,
1
1
3, 4
,
1
5
,
1
6
,
1
8
, etc ... ) (Tracing paper may help).
a
b
c
d
e
f
National 4 Book N4-2
this is page 40
Chapter 3 - Symmetry
3.
g
h
i
j
k
l
Rotating a Given Shape by a
1
2
Turn
The red dot in this diagram has to be
the centre of symmetry when the
shape is rotated 12 turn about it.
•
•
180° rotation clockwise
•
180°
new position
Exercise 3
1.
(You will need a ruler or straight edge and
a
Copy this rectangle onto
1
centimetre squared paper.
2
b
Rotate it by a
2.
National 4 Book N4-2
1
2
1
2
cm squared paper).
•
turn around the red dot.
•
a
Make a second copy of this rectangle.
b
This time, rotate it by half a turn
around the new dot.
this is page 41
Chapter 3 - Symmetry
3.
4.
a
Copy the letter “T” carefully onto
1
centimetre squared paper.
2
b
Rotate it by half a turn around the dot.
Copy each of the following shapes onto
squared paper and rotate each by
a
1
2
1
2
•
centimetre
a turn around the dot :–
b
c
•
d
e
•
g
f
•
•
h
•
5.
•
•
i
•
•
Here is how to rotate a complicated shape around a point, using mathematics.
a
Copy this shape carefully onto squared paper.
b
Look at corner 1.
It is 7 boxes to the left of Point P.
•
2
When rotated, it will end up 7 boxes
to the right of P. (Show this).
c
d
Corner 3 is “4 boxes left and 6 boxes
up” from P.
•
•4
Corner 2 is “7 boxes left and 6
boxes up” from P.
It will end up “7 boxes right and
6 boxes down” from P. (Show this).
180°
3
•6
5
•
•P
•
1
It will end up “4 boxes right and 6 boxes down” from P. (Show this).
National 4 Book N4-2
this is page 42
Chapter 3 - Symmetry
5.
6.
e
Corner 4 is “..... boxes left and 4 boxes up” from P.
It will end up “..... boxes right and 4 boxes ....”. from P. (Show this).
f
Corner 5 is “..... boxes left and ..... boxes up” from P.
It will end up “..... boxes ..... and ..... boxes .....” from P. (Show this).
g
Corner 6 is “..... boxes up” from P.
It will end up “..... boxes down” from P. (Show this).
h
Join up your dots including P to find its new position.
Draw each of the following and use the Counting method to find each new corner
when the shape is rotated by 180° around Point P.
P
a
b
•
•P
c
d
P
•
•P
e
f
P
National 4 Book N4-2
•P
•
this is page 43
Chapter 3 - Symmetry
Order of Symmetry
turn symmetry is said to have order of symmetry of 2.
A shape which has
1
2
1
3
A shape which has
1
4
turn symmetry is said to have order of symmetry of 4.
A shape which has
1
10
A shape which has
turn symmetry is said to have order of symmetry of 3.
turn symmetry is said to have order of symmetry of 10.
Exercise 4
1.
State the order of symmetry of a shape which has a turn symmetry of :–
a
2.
1
5
b
c
1
23
d
1
147
.
State the order of symmetry and the turn symmetry for each of these shapes :–
a
square
b
e
3.
1
9
pentagon
f
Copy each of the following shapes onto
1
2
c octagon
d
g
h
equilateral triangle
centimetre squared paper.
Complete each shape so that it has rotational symmetry about O in the given order :–
a
b
•O
order of symmetry of 4
e
•O
f
order of symmetry of 4
National 4 Book N4-2
•O
order of symmetry of 4
h
•O
order of symmetry of 4
•O
order of symmetry of 2
g
•O
•O
order of symmetry of 2
d
c
order of symmetry of 4
i
•O
order of symmetry of 4
this is page 44
•O
order of symmetry of 4
Chapter 3 - Symmetry