A figure has rotational symmetry if it looks identical after being rotated by some angle less than 360° about a central point. The order of rotational symmetry is the number of distinct positions where the figure looks the same during a full rotation.
If you turn it and it still fits exactly, it has rotational symmetry.
Showing a random 20 of 50 problems.
Example 1
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Does an isosceles (non-equilateral) triangle have any rotational symmetry?
Example 2
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What is the order of rotational symmetry of a (non-square) rectangle?Non-square rectangle: only a 180° rotation maps it onto itself — order 2.
Example 3
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Does a rectangle (non-square) have rotational symmetry? Give the order and smallest angle.
Example 4
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Equilateral triangle ABC is centred at the origin. A 120° counterclockwise rotation maps A→B. What does C map to, and what is the order of symmetry?Equilateral triangle ABC centred at O. A 120° CCW rotation maps A→B, B→C, C→A.
Example 5
hard
A regular n-gon has rotational symmetry of order n. Which n gives a smallest rotation angle of 30°?
Example 6
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What is the order of rotational symmetry of a square?Square: maps onto itself every 90° — rotational symmetry of order 4.
Example 7
challenge
Why is rotational symmetry an example of geometric invariance?
Example 8
easy
Does the letter 'O' have rotational symmetry? If yes, what is its order?
Example 9
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What is the order of rotational symmetry of a regular hexagon?Regular hexagon: 360° ÷ 6 = 60° minimum rotation — order 6.
Example 10
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Explain why snowflakes typically show 6-fold rotational symmetry, linking it to molecular structure.
Example 11
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A figure maps onto itself at 60°, 120°, 180°, 240°, 300°, and 360°. What is its order of rotational symmetry?
Example 12
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Does a regular n-gon's order of rotational symmetry equal n?
Example 13
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How many angles strictly between 0° and 360° map a figure of rotational order 7 onto itself?
Example 14
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What is the order of rotational symmetry of a regular pentagon?
Example 15
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A regular polygon has smallest rotation angle 24°. How many sides does it have?
Example 16
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Why does a recycling symbol (three arrows) have order 3 rotational symmetry?
Example 17
hard
A pinwheel has 4 identical blades arranged around a center. What is its rotational symmetry order and smallest angle?
Example 18
easy
What does it mean for a figure to have rotational symmetry?
Example 19
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Which letter has rotational symmetry of order 2: 'A' or 'Z'?
Example 20
easy
What is the smallest rotation angle that maps a regular octagon onto itself?