Draw a regular hexagon and join all its diagonals. How many lines of symmetry does the resulting figure have?
Answer
6
The correct answer is 6 — Therefore the resulting figure also has 6 lines of symmetry.
Step-by-step solution
- Recognise that drawing all diagonals of a regular hexagon creates a star-shaped figure but the outer shape remains a regular hexagon.
- The figure retains all reflectional symmetries of the original hexagon.
- A regular hexagon possesses 6 lines of symmetry.
- Therefore the resulting figure also has 6 lines of symmetry.
Common mistake: Assuming the added diagonals reduce symmetry
Concept tested: Symmetry of regular polygons after adding diagonals
Published · How this solution was prepared and checked
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