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Symmetry in 2D Shapes
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Symmetry in 2D Shapes
Rawiri, Isla and Tevita are designing a set of geometric emblems for a ferry trip. Complete each task to help them check which designs have line symmetry. A line of symmetry divides a shape into two matching mirror halves. Consider exact shape and size, not just appearance.
Spot the symmetry
1.Which statement best defines a line of symmetry in a 2D shape?
- It divides the shape into two matching mirror-image halves.
- It divides the shape into two halves with equal area, even if their outlines differ.
- It is any line drawn from one vertex to another.
- It is the longest side of the shape.
2.A square has how many lines of symmetry?
3.The ferry emblem is an equilateral triangle. How many lines of symmetry does it have?
4.A non-square rectangle is turned on the page. How many lines of symmetry does it have?
- 0
- 1
- 2
- 4
Test and explain
5.True or false: Every line that cuts a shape into two equal-area parts is a line of symmetry. Explain briefly.
6.A regular pentagon has five equal sides and five equal angles. How many lines of symmetry does it have?
7.Rawiri claims that a parallelogram always has a line of symmetry. Is he correct? Give a reason or a counterexample.
8.Match each shape to its number of lines of symmetry: (a) non-square rectangle, (b) regular hexagon, (c) circle, (d) scalene triangle.
- Non-square rectangle
- Regular hexagon
- Circle
- Scalene triangle
- 0
- 2
- 6
- Infinitely many
Design an emblem
9.Draw a 2D emblem for the ferry that has exactly one line of symmetry. Mark the line, then explain how you know the two sides match. Your drawing must be your own.
10.Isla reflects one half of a design across a vertical line to complete the other half. Name one detail that must stay unchanged during the reflection and one detail that changes position.
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