A free Sec 1 G1 Maths worksheet on symmetry: 15 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.
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Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1
The diagram shows a kite. State whether the dashed line is a line of symmetry of the shape.
Answer[1]
2
The diagram shows the letter L. Write down the number of lines of symmetry of the shape.
Answer[1]
3
The diagram shows the letter M. Write down its order of rotational symmetry.
Answer[1]
4
The diagram shows a pencil shape. Write down the number of lines of symmetry of the shape.
Answer[1]
5
The diagram shows an equilateral triangle. Write down its order of rotational symmetry.
Answer[1]
6
The diagram shows a house shape. Write down its order of rotational symmetry.
Answer[1]
7
The diagram shows a pinwheel. Write down the number of lines of symmetry of the shape.
Answer[1]
8
The diagram shows the letter U. Write down the number of lines of symmetry of the shape.
Answer[1]
9
The diagram shows a square. Write down its order of rotational symmetry.
Answer[1]
10
The diagram shows a six-pointed star. State whether the dashed line is a line of symmetry of the shape.
Answer[1]
11
The diagram shows a regular decagon. Find the smallest angle through which it can be rotated about its centre to look exactly the same.
Answer°[2]
12
The diagram shows a parallelogram. Find the smallest angle through which it can be rotated about its centre to look exactly the same.
Answer°[2]
Section B
13
(a)The diagram shows a plus sign. Write down the number of lines of symmetry of the shape.
Answer (a)[1]
(b)The diagram shows the letter E. State whether the dashed line is a line of symmetry of the shape.
Answer (b)[1]
(c)The diagram shows an equilateral triangle. Write down its order of rotational symmetry.
Answer (c)[1]
(d)The diagram shows a parallelogram. Find the smallest angle through which it can be rotated about its centre to look exactly the same.
Answer (d)°[2]
14
(a)The diagram shows a bow-tie shape. Write down the number of lines of symmetry of the shape.
Answer (a)[1]
(b)The diagram shows a regular nonagon. Find the smallest angle through which it can be rotated about its centre to look exactly the same.
Answer (b)°[2]
(c)The diagram shows a bow-tie shape. Find the smallest angle through which it can be rotated about its centre to look exactly the same.
Answer (c)°[2]
15
(a)The diagram shows a square. Write down the number of lines of symmetry of the shape.
Answer (a)[1]
(b)The diagram shows the letter T. Write down its order of rotational symmetry.
Answer (b)[1]
(c)The diagram shows a parallelogram. Find the smallest angle through which it can be rotated about its centre to look exactly the same.
Answer (c)°[2]
(d)The diagram shows a regular pentagon. Find the smallest angle through which it can be rotated about its centre to look exactly the same.
Answer (d)°[2]
END OF PAPER
Answers and worked solutions
Question 1
Answer: NO[1]
Each corner on one side must land exactly on a corner on the other side, and each side on a side.No: the two halves do not match when folded, so the dashed line is not a line of symmetry.
Question 2
Answer: Number of lines of symmetry=0[1]
Lines of symmetry: none: the two arms are different lengths.Number of lines of symmetry=0
Question 3
Answer: Order=1[1]
It looks the same only after a full turn.Order=1
Question 4
Answer: Number of lines of symmetry=1[1]
Lines of symmetry: the line along the pencil.Number of lines of symmetry=1
Question 5
Answer: Order=3[1]
It looks the same every third of a turn.Order=3
Question 6
Answer: Order=1[1]
It looks the same only after a full turn.Order=1
Question 7
Answer: Number of lines of symmetry=0[1]
Lines of symmetry: none: the blades all lean the same way.Number of lines of symmetry=0
Question 8
Answer: Number of lines of symmetry=1[1]
Lines of symmetry: the upright line down the middle.Number of lines of symmetry=1
Question 9
Answer: Order=4[1]
It looks the same every quarter turn.Order=4
Question 10
Answer: NO[1]
Each corner on one side must land exactly on a corner on the other side, and each side on a side.No: the two halves do not match when folded, so the dashed line is not a line of symmetry.
Question 11
Answer: Angle=36∘ °[2]
It looks the same every tenth of a turn.Order=10Angle=10360∘Angle=36∘
Question 12
Answer: Angle=180∘ °[2]
It looks the same every half turn.Order=2Angle=2360∘Angle=180∘
Question 13
(a)Answer: Number of lines of symmetry=4[1]
Lines of symmetry: one along each arm and the two diagonals.Number of lines of symmetry=4
(b)Answer: YES[1]
Each corner on one side must land exactly on a corner on the other side, and each side on a side.Yes: the two halves fold exactly onto each other, so the dashed line is a line of symmetry.
(c)Answer: Order=3[1]
It looks the same every third of a turn.Order=3
(d)Answer: Angle=180∘ °[2]
It looks the same every half turn.Order=2Angle=2360∘Angle=180∘
Question 14
(a)Answer: Number of lines of symmetry=2[1]
Lines of symmetry: one through the two triangles' tips and one across the middle.Number of lines of symmetry=2
(b)Answer: Angle=40∘ °[2]
It looks the same every ninth of a turn.Order=9Angle=9360∘Angle=40∘
(c)Answer: Angle=180∘ °[2]
It looks the same every half turn.Order=2Angle=2360∘Angle=180∘
Question 15
(a)Answer: Number of lines of symmetry=4[1]
Lines of symmetry: the two diagonals and the two lines joining the middles of opposite sides.Number of lines of symmetry=4
(b)Answer: Order=1[1]
It looks the same only after a full turn.Order=1
(c)Answer: Angle=180∘ °[2]
It looks the same every half turn.Order=2Angle=2360∘Angle=180∘
(d)Answer: Angle=72∘ °[2]
It looks the same every fifth of a turn.Order=5Angle=5360∘Angle=72∘