Is equilateral trapezium possible?

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Q.Is equilateral Trapezium possible?

The defination of Trapezium :A quadrilateral with one pair of parallel sides.

If we have a trapezium that have equal sides,it becomes a rhombus (& contradicts it's own defination). This implies that equilateral trapezium is not possible.

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2 Answers

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A quadrilateral that is both a trapezium (in those countries that call football soccer: a trapezoid) and a rhombus is a square. Note that "one pair" i the definition of trapezium is understood as "at least one pair"

Apart from that, the term "equilateral (or: isosceles) tapezium" is used for a trapezium where (only) the non-parallel (or not necessarily parallel) pair of sides are of the same langth.

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The definition of trapezium states that it has one pair of parallel sides but it does not say that it must have one pair of non parallel sides. And hence the equilateral trapezium is the rhombus.

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