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Exploring Symmetry in Shapes

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Exploring Symmetry in Shapes

At a fishing harbour, Nathan, Mere and Zoe are designing signs for a new wharf. Use reflection and rotational symmetry to solve their design challenges. For drawings, use squared paper or the drawing boxes; label each line or centre of rotation.

Spot the Symmetry

Think about how shapes match when reflected or turned.

1.A regular hexagonal warning sign is reflected in a mirror line through two opposite vertices. How many lines of symmetry does a regular hexagon have altogether?

2.Mere needs a flag shape with exactly one line of symmetry. Which shape is the best choice?

A non-equilateral isosceles triangle
A square
A circle
A regular pentagon

3.A design is folded along a line and both sides match exactly. What does this tell you about the line?

4.Nathan turns a square sign around its centre. Which statement about its rotational symmetry is correct?

It matches itself after a quarter-turn, so its order is 4.
It matches itself only after a full turn, so its order is 1.
It matches itself after a half-turn, so its order is 2.
It never matches itself.

Turn, Reflect and Explain

Show how the shapes behave, then justify your thinking.

5.A rectangular wharf information panel is not a square. State how many lines of symmetry it has and its rotational symmetry order.

6.A regular octagonal buoy label is turned about its centre. Complete both facts: it has lines of symmetry and rotational symmetry of order .

7.Zoe says, “A shape has rotational symmetry only if it has a line of symmetry.” Is Zoe correct? Give an example to support your answer.

8.On squared paper, draw a four-pointed harbour compass emblem that has at least 2 lines of symmetry. Mark every line of symmetry you have included.

9.Design a simple wharf logo that has rotational symmetry of order 2 but no line of symmetry. Sketch it and explain how a half-turn tests its rotational symmetry.

10.A boat-builder uses a symmetrical hull outline, while a propeller uses rotational symmetry. Explain one practical advantage of each type of symmetry in these designs.