Symmetry & Shape Properties
25 Class 6 IMO Mathematics Olympiad practice questions on symmetry & shape properties, part of the Geometry & Spatial Thinking topic area. Every question below includes the correct answer and a full explanation.
Practice this topic interactively →1. How many lines of symmetry does a square have?
- A.2
- B.3
- C.4
- D.5
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Answer: C. 4
A square has 4 lines of symmetry.
2. How many lines of symmetry does an equilateral triangle have?
- A.1
- B.2
- C.3
- D.4
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Answer: C. 3
An equilateral triangle has 3 lines of symmetry, one through each vertex.
3. How many lines of symmetry does a circle have?
- A.0
- B.1
- C.4
- D.Infinite
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Answer: D. Infinite
Any line through a circle's centre is a line of symmetry, so it has infinitely many.
4. How many sides does a hexagon have?
- A.5
- B.6
- C.7
- D.8
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Answer: B. 6
A hexagon has 6 sides.
5. How many sides does a regular pentagon have?
- A.4
- B.5
- C.6
- D.7
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Answer: B. 5
A pentagon has 5 sides.
6. Which of these shapes has no lines of symmetry?
- A.Parallelogram
- B.Square
- C.Circle
- D.Rectangle
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Answer: A. Parallelogram
A general parallelogram (not a rectangle or rhombus) has no lines of symmetry.
7. How many vertices does a cube have?
- A.4
- B.6
- C.8
- D.12
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Answer: C. 8
A cube has 8 vertices (corners).
8. How many faces does a cube have?
- A.4
- B.6
- C.8
- D.12
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Answer: B. 6
A cube has 6 faces.
9. How many lines of symmetry does a regular 5-sided polygon have?
- A.6
- B.4
- C.10
- D.5
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Answer: D. 5
A regular polygon has as many lines of symmetry as it has sides: 5.
10. How many diagonals does a polygon with 5 sides have?
- A.6
- B.4
- C.5
- D.7
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Answer: C. 5
5 × (5 − 3) ÷ 2 = 5.
11. How many lines of symmetry does a regular 4-sided polygon have?
- A.3
- B.8
- C.4
- D.5
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Answer: C. 4
A regular polygon has as many lines of symmetry as it has sides: 4.
12. How many lines of symmetry does a regular 8-sided polygon have?
- A.8
- B.16
- C.7
- D.9
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Answer: A. 8
A regular polygon has as many lines of symmetry as it has sides: 8.
13. How many diagonals does a polygon with 10 sides have?
- A.37
- B.35
- C.34
- D.36
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Answer: B. 35
10 × (10 − 3) ÷ 2 = 35.
14. Which property is shared by a square and an equilateral triangle?
- A.All angles are right angles
- B.All sides are equal
- C.They have four sides
- D.They have two lines of symmetry
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Answer: B. All sides are equal
A square has 4 equal sides and an equilateral triangle has 3 equal sides — both have all sides equal. The other options don't hold for both shapes.
15. How many lines of symmetry does a regular pentagon have?
- A.3
- B.4
- C.5
- D.6
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Answer: C. 5
A regular polygon has as many lines of symmetry as it has sides — 5 for a pentagon.
16. Which of these letters has a horizontal line of symmetry?
- A.A
- B.B
- C.M
- D.T
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Answer: B. B
B looks the same when folded along a horizontal line through its middle. A, M, and T only have vertical symmetry.
17. A rectangle that is not a square has how many lines of symmetry?
- A.0
- B.1
- C.2
- D.4
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Answer: C. 2
A non-square rectangle has 2 lines of symmetry: one horizontal, one vertical.
18. Which shape has exactly one line of symmetry?
- A.Scalene triangle
- B.Isosceles triangle
- C.Equilateral triangle
- D.Square
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Answer: B. Isosceles triangle
An isosceles triangle has exactly one line of symmetry, down the middle from its apex.
19. How many lines of symmetry does a regular octagon have?
- A.6
- B.7
- C.8
- D.9
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Answer: C. 8
A regular polygon has as many lines of symmetry as it has sides — 8 for an octagon.
20. How many lines of symmetry does a regular hexagon have?
- A.3
- B.4
- C.5
- D.6
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Answer: D. 6
A regular hexagon has 6 lines of symmetry.
21. A regular polygon has 5 lines of symmetry. How many sides does it have?
- A.4
- B.5
- C.6
- D.10
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Answer: B. 5
For a regular polygon, the number of lines of symmetry equals the number of sides — so it has 5 sides.
22. How many lines of symmetry does a regular 6-sided polygon have?
- A.7
- B.12
- C.5
- D.6
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Answer: D. 6
A regular polygon has as many lines of symmetry as it has sides: 6.
23. How many diagonals does a polygon with 4 sides have?
- A.2
- B.3
- C.1
- D.4
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Answer: A. 2
4 × (4 − 3) ÷ 2 = 2.
24. How many diagonals does a polygon with 6 sides have?
- A.10
- B.11
- C.9
- D.8
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Answer: C. 9
6 × (6 − 3) ÷ 2 = 9.
25. How many diagonals does a polygon with 9 sides have?
- A.28
- B.27
- C.26
- D.29
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Answer: B. 27
9 × (9 − 3) ÷ 2 = 27.