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A trapezium is a quadrilateral with at least one pair of parallel sides. A quadrilateral has vertices, taken in order, at A(1, 1), B(9, 1), C(7, 5) and D(3, 5). Which description fits it best?

Competition practiceGeometry
  • AAn isosceles trapezium
  • BA parallelogram
  • CA rectangle
  • DA kite

Step-by-Step Solution

AB runs along with length 8, and DC runs along with length 4, so AB and DC are parallel — one pair of parallel sides, which satisfies the definition. They are unequal, so it is not a parallelogram. The other two sides are AD = √ √20 and BC = √ = √20, equal to each other, so the trapezium is isosceles. It is not a kite, since a kite has two pairs of equal adjacent sides.
Answer: A) An isosceles trapezium

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