A
S1 Revision/Notes - Symmetry
Line Symmetry
A shape has a line of symmetry (or axes of symmetry) if, when you fold the shape over the
line, the 2 halves exactly match.
Some shapes have more than 1 line of symmetry. For example:
3 lines of symmetry
2 lines of symmetry
5 lines of symmetry
To complete the missing half of a symmetrical picture we reflect the image across the line of
symmetry.
We also use reflection when creating symmetrical images on a coordinate grid. For example
we can reflect an image across the x-axis or across the y-axis.
Reflecting across the x-axis
Reflecting across the y-axis
Rotational Symmetry
Some shapes have no LINES of symmetry, but they do have rotational symmetry. If we rotate
an image around the centre point, the number of times the shape will fit back into its
original outline is called its order of rotational symmetry.
For example this shape will fit into its outline twice, so we say it has rotational symmetry of
order 2.
Another example is a triangle; this shape will fit into its outline 3 times so we say it has
rotational symmetry of order 3.
Please attempt the questions below at the appropriate level:
2nd & 3rd Level Questions
Q1.. How many lines of symmetry can you draw on these shapes:
a)
b)
c)
d)
Q2. Which of the following shapes have an axes of symmetry?
Q3, Draw these shapes in your jotter and fill in all possible lines of symmetry.
e)
Q4. Copy and complete the following shapes:
4th Level Questions
Q1. State the order of rotational symmetry of the following shapes:
Q2. Write down the coordinates of each point and its image when reflected in the x-axis:
Q3. Write down the coordinates of each point from the diagram above when reflected in the
y-axis.
Q4. A triangle has vertices at S(1, 3), T(4, 6) and V(3, 2).
i) Draw this triangle on a coordinate grid (4 quadrants)
ii) Draw the image of the triangle when reflected in the x-axis.
Q5 Plot the following points on a coordinate grid (4 quadrants):
G(1, 6), H(5, 5), I(1, -4), J(-3, 3) , K(-2, -5)
i) Reflect this image in the y-axis and write down the coordinates of the reflected points.