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Matariki Star Pattern Geometry

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Matariki Star Pattern Geometry

Explore symmetry, angles and shapes through Matariki-inspired star patterns. Matariki is a star cluster important in te ao Māori. Different traditions describe the cluster in different ways. Show your reasoning where asked.

Spot the geometry

Answer each question using the information given. A regular polygon has equal sides and equal angles.

1.A designer arranges seven stars evenly around a circle. What is the angle between neighbouring stars at the centre? Give your answer to the nearest tenth of a degree.

2.A regular five-pointed star has five matching points. Which shape has five sides and could sit in the middle of a five-pointed star?

A triangle
A pentagon
A hexagon
An octagon

3.A regular five-pointed star is reflected across a line through its centre and one point. What kind of symmetry does this show?

Rotational symmetry
Line symmetry
No symmetry
Translation symmetry

4.The five outer points of a regular star are evenly spaced around a full turn. What is the angle between neighbouring points at the centre?

5.A six-pointed star is made by laying two identical equilateral triangles over one another. What is the size of each angle in an equilateral triangle?

30°
45°
60°
90°

6.When a pattern is folded along a vertical line through its centre, its two halves do not match. True or false: the pattern has line symmetry along that line.

TrueFalse

Plan a star pattern

Use the visual guides below to reason about turns and design your own pattern.

7.A six-pointed pattern repeats after equal turns. Complete the angle around the centre: one full turn is 360°, so each of six equal turns is degrees.

8.A constellation designer connects six evenly spaced points on a circle, joining every second point to make two triangles. What shape do the two outlines make together?

9.Draw a Matariki-inspired pattern with at least five stars. Include one line of symmetry, and label one angle you can identify. Your design may represent a place, memory or group that matters to you.

10.A six-pointed star pattern looks unchanged after a 60° turn. How many times will it match itself during one complete 360° turn, including the starting position? Explain with a calculation.