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A trapezium is defined as a quadrilateral with at least one pair of parallel sides. Using that definition, which of the following statements is FALSE?

Competition practiceGeometry
  • AEvery rectangle is a trapezium
  • BEvery square is a trapezium
  • CEvery rhombus is a trapezium
  • DA trapezium has exactly one pair of parallel sides

Step-by-Step Solution

Rectangles, squares and rhombuses are all parallelograms, so each has two pairs of parallel sides — certainly at least one pair — and all three are trapeziums under this definition. The word "exactly" is what makes the last statement false: the definition says at least one pair, so a trapezium is allowed to have two.
Answer: D) A trapezium has exactly one pair of parallel sides

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