Question 1
1(a):
Which lines on the diagram are the lines of symmetry for the rectangle?
ANSWER: Multiple Choice (Type 1)
A: A & C
B: A & B
C: C & D
D: B & D
Answer: B
Workings:
A rectangle has two lines of symmetry, one horizontal and one vertical, intersecting at the centre. These are lines A and B in the diagram.
Marks = 2
1(b):
State the order of rotational symmetry of the shape below.
ANSWER: Simple Text Answer
Answer: 8
Workings:
The image has 8 identical points, evenly spaced around a circle. This means that if we rotate it so a different point is pointing directly upwards it will look exactly the same.
Marks = 1
Question 2
2(a):
Which shape has the most lines of symmetry.
ANSWER: Multiple Choice (Type 1)
A: Shape A
B: Shape B
C: Shape C
Answer: C
Workings:
Shape A has three lines of symmetry, shape B has 4 lines of symmetry and shape C has 7 lines of symmetry.
Marks = 1
2(b):
Which of these triangles has rotational symmetry order 3?
ANSWER: Multiple Choice (Type 1)
A: Triangle A
B: Triangle B
C: Triangle C
D: Triangle D
Answer: A
Workings:
There are three different rotations that can be made of triangle A so that it look exactly the same.
Marks = 1
Question 3
3(a):
How many lines of symmetry does an Octagon have?
ANSWER: Simple Text Answer
Answer: 8
Workings:
An Octagon has 8 lines of symmetry, 4 connecting opposite the sides and 4 connecting the opposite corners.
Marks = 1
3(b):
List the following rectangular flags in ascending order of lines of symmetry.
Make sure to write the country exactly as it appears in the question.
ANSWER: Multiple Answers (Type 1)
Answer: Least = Brazil, Middle = Antigua and Barbuda, Most = Georgia
Workings:
Brazil has no lines of symmetry, Antigua and Barbuda has one vertical line of symmetry down the middle, Georgia has two lines of symmetry, one vertical line down the middle and one horizontal line across the middle.
Marks = 1
3(c):
State the order of rotational symmetry for the following shape.
ANSWER: Simple Text Answer
Answer: 2
Workings:
The image can be rotated 180\degree to give the same image.
Marks = 1
Question 4
4(a):
How many lines of symmetry does a regular polygon with n sides have?
Give your answer in terms of n.
ANSWER: Simple Text Answer
Answer: n
Workings:
For shapes with an odd number of sides, each corner has a line of symmetry to the opposite side giving a total of n. For shapes with an even number of sides \dfrac{n}{2} lines connect opposite corners and \dfrac{n}{2} lines connect opposite sides giving a total of n.
Marks = 1
4(b):
State the order of rotational symmetry of a square.
ANSWER: Simple Text Answer
Answer: 4
Workings:
If you rotate a square 360\degree around the centre it will look exactly the same 4 times at 90\degree intervals, so the order of rotational symmetry is 4.
Marks = 1
4(c):
Which of these gives a net of a dice with order 2 rotational symmetry and 0 lines of reflection?
ANSWER: Multiple Choice (Type 1)
Answer: A
Workings:
Rotating A by 180\degree will give an identical image. It has no lines of symmetry. Shapes B and D both have one line of reflection, so it can’t be them. Shape C has no lines of symmetry but also no rotational symmetry. So the answer must be A.
Marks = 2
Question 5
5(a):
Name the type of triangle that can have one line of reflective symmetry.
ANSWER: Multiple Choice (Type 1)
A: Equilateral
B: Isosceles
C: Scalene
Answer: B
Workings:
An Isosceles triangle has two sides of the same length, so a line of symmetry will run between them. An Equilateral has 3 lines of symmetry and a Scalene has no lines of symmetry.
Marks = 1
5(b):
The descriptions of 4 shapes are shown below.
Match each of the following descriptions to the correct shape it’s describing.
Enter the letter of the shape, ensuring you use a capital letter.
ANSWER: Multiple Answers (Type 1)
Answer: P = B, Q = E, R = D, S = C
Workings:
The Parallelogram in image B has two orders of rotational symmetry and no lines of symmetry.
The Quadrilateral in image E has 1 order of rotational symmetry and 1 vertical line of symmetry.
The Rhombus in image D has 2 orders of rotational symmetry and 2 lines of symmetry, one horizontal and one vertical.
The Square in image C has 4 orders of rotational symmetry and 4 lines of symmetry, one horizontal, one vertical and two diagonal.
Marks = 3
Question 6
Jenn is exploring symmetry. She is drawing a shape. She says:
“The shape I am drawing is a regular polygon.
The sum of its interior angles add up to 540 degrees.”
6(a):
What shape is she drawing?
ANSWER: Multiple Choice (Type 1)
A: Triangle
B: Rectangle
C: Pentagon
D: Hexagon
Answer: C
Workings:
The sum of the interior angles in an n-sided polygon can be summarised by the equation (n-2)\times 180.
This can be rearranged to n=\dfrac{sum of angles}{180}+2.
In this case it gives us n=\dfrac{540}{180}+2=5
So the shape being described is a Pentagon.
Marks = 1
6(b):
What is the order of rotational symmetry of Jenn’s shape?
ANSWER: Simple Text Answer
Answer: 5
Workings:
A Pentagon has an odd number of sides, so each corner connects to the opposite side, giving us a rotational symmetry order of 5.
Marks = 1
6(c):
Jenn starts to look at the symmetry of letters.
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
There are four letters with at least two lines of symmetry.
Which are they?
State your answer with the letter as a capital.
ANSWER: Multiple Answers (Type 1)
Answer: H, I, O, X
Workings:
The letters H, I & X have 2 lines of symmetry while O has an infinite number.
Marks = 1
6(d):
Which of these is a pair of letters where both have order of rotational symmetry 2.
ANSWER: Multiple Choice (Type 1)
A: Y & H
B: I & M
C: T & Z
D: S & X
Answer: D
Workings:
Rotating both the letters S & X by 180\degree will give an identical image, so both have rotational symmetry 2.
Marks = 1