Are the bases of a trapezoid always equal?

| August 6, 2021 | education

A trapezoid is a quadrilateral in which two sides are parallel (the bases of the trapezoid), and the other two are not parallel (the sides of the trapezoid).

Suppose the bases of the trapezoid are equal. Then we have a quadrangle in which the two sides are equal and parallel. This is the first sign of a parallelogram. This quadrilateral is a parallelogram, which means that its sides (by definition) are pairwise parallel. However, this violates the definition of a trapezoid, in which two opposite sides are necessarily not parallel (lateral).

Thus: no, the bases of the trapezoid are by no means equal!

By the way, here its sides (hips of the trapezoid) can be the same – the trapezoid will become isosceles. But not all trapezoids are required to be isosceles.



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