12/16/2023 0 Comments Isosceles trapezoid definition math![]() (Note here that the center trapezoid is actually a rectangle…God forbid!!) But under the exclusive definition, you would have to change its name to the “trapezoidal and/or rectangular approximation method,” or perhaps ban people from doing the trapezoidal method on problems like this one: Approximate using the trapezoidal method with 5 equal intervals. The trapezoidal approximation method in Calculus doesn’t fail when one of the trapezoids is actually a rectangle.Instead, define an isosceles trapezoid as having base angles congruent, or equivalently, having a line of symmetry. Those texts define an isosceles trapezoid has having both legs congruent, which would make a parallelogram an isosceles trapezoid. With the exception of the definition that some texts use for an isosceles trapezoid. No other definitions break when you use the inclusive definition.It’s true! The area formula works fine for a parallelogram, rectangle, rhombus, or square. The area formula for a trapezoid still works, even if the legs are parallel.Likewise, parallelograms, rectangles, rhombuses, and squares should all be special cases of a trapezoid. All other quadrilaterals are defined in the inclusive way, so that quadrilaterals “beneath” them inherit all the properties of their “parents.” A square is a rectangle because a square meets the definition of a rectangle.I finish by offering the following list of reasons why the inclusive definition is better (can you suggest more reasons?): In order for (A) and (C) to be trapezoids, under the exclusive definition, you must prove that two sides are parallel AND the two remaining sides are not parallel (and you can’t assume that from the picture…especially for (C)!).Ĭan you see the absurdity of the exclusive definition now? ![]() ![]() But it gets better: If you were using the the exclusive definition, then NONE of these are trapezoids. Not so fast!! If you’re using the inclusive definition, then the correct answers are actually (A), (B), (C), (D), and (E). So the test question above was easy, right? Quadrilaterals (A) and (C) are trapezoids, I hear you say. “A quadrilateral with at least one pair of parallel sides.” The definition should be made inclusive, and read: “A quadrilateral with one and only one pair of parallel sides.” I believe that instead of this typical textbook definition (the “exclusive definition” we’ll call it) that reads: Which of the following quadrilaterals are trapezoids?īefore giving the answer, let me first just remind you about my very strongly held position. See if you can answer the question without any help. Let’s start with the following easy test question. So I thought I’d come out of my shell and post something…and of course I always have something to say about trapezoids :-). I’ve been taking a break from blogging, as I usually do in the summer. ![]() I’m writing about trapezoids again (having written passionately about them here and here previously). ![]()
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