![]() ![]() On the other hand, using an inclusive definition of trapezoids ( at leastone pair of parallel sides) creates the far more consistent relationship structure shown below. Interestingly, this same area formula also applies (with acknowledgement that ) to parallelograms, rhombi, rectangles, and squares, a “coincidence” ignored by proponents of the exclusive definition. With nothing guaranteed about the non-parallel or congruent sides, about all you can claim is its area formula: where and are the parallel bases and ht is the height. The classification question has been discussed by Zalman Usiskin and others, but I’ll attempt a portion of my own micro-version around trapezoid classifications here.įirst, pure trapezoids (those that can’t be called anything more specific under either definition) have precious few properties. I agree completely because once definitions are accepted–especially in mathematics–they absolutely drive and constrain any and all logical conclusions one logically is able to reach. ![]() Isosceles trapezoid definition free#Who cares, some may ask? From one perspective, everyone is perfectly free to use either definition, but I agree with the contributor who argues that part of the discussion ought to be about what makes a definition in mathematics. ![]() There have been many discussions about the importance of definitions in mathematics, and in this thread, the contributors rightly noted that the inclusive definition makes parallelograms a type of trapezoid (exactly like squares are a type of rectangle), while the exclusive definition expressly forbids this because parallelograms don’t have exactly one pair of parallel sides. There was a recent debate on the AP Calculus EDG on the definition of a trapezoid, specifically whether a trapezoid has “exactly one pair of parallel sides” (the exclusive definition) or “at least one pair of parallel sides” (the inclusive definition). ![]()
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