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Consider a rhombus that is not a square. Which description of its symmetry is correct?

Competition practiceGeometry
  • A4 lines of symmetry and rotational symmetry of order 4
  • B2 lines of symmetry and rotational symmetry of order 4
  • C2 lines of symmetry and rotational symmetry of order 2
  • D1 line of symmetry and rotational symmetry of order 2

Step-by-Step Solution

Only the two diagonals are lines of symmetry for a rhombus; the lines through the midpoints of opposite sides are axes of symmetry only when the rhombus is a square. Turning it through 180° about the centre maps it onto itself, and a quarter turn does not, so the rotational symmetry has order 2.
Answer: C) 2 lines of symmetry and rotational symmetry of order 2

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