Several world have doubted me around the definition of a trapezoid that shows up in math Mammoth grade 5 curriculum:


You can easily find other interpretations for a trapezoid which indicate it only has ONE pair that parallel sides. So, people get confused.

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This is just one of those rare instances whereby there exist two varieties of interpretations for a shape. The one I offered is an "inclusive" definition, due to the fact that according come it, squares and rectangles and also parallelograms are INCLUDED... They are trapezoids also.

But several of my customers have learned the "exclusive" definition, which says a trapezoid has specifically one pair of parallel present (not two). Making use of this definition, squares, parallelograms, and also rectanges won"t qualify.

Mathematicians favor the inclusive meaning (the one that says "at least one pair that parallel lines"). Why? since it makes their theorems shorter to state. If other is true of every trapezoids, the one word "trapezoid" captures all the forms with at the very least one pair of parallel lines, and they don"t have to state the it is true because that "trapezoids, parallelograms, rhombi, rectangles, and squares". It simply makes points simpler.

The same is true in the case of a square matches rectangle. Tiny children regularly think in terms of the exclusive definitions, and also view squares as no rectangles. To them, a rectangle cannot have actually all equal sides. But, as you more than likely know, the inclusive meaning (a rectangle is a form with 4 sides and also four ideal angles) is the prevailing one in the adult world, and squares room classified together rectangles.

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The factor I supplied the inclusive definition in math Mammoth wasn"t therefore much due to the fact that of theorems regarded trapezoids (we don"t really study any kind of in elementary math). The was due to the fact that that an interpretation allows us to attract this neat quadrilateral classification, or tree diagram:


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Notice, the trapezoid is presented together ABOVE, or together a "parent" that a parallelogram. In other words, a parallelogram is a "child" of a trapezoid. It method all parallelograms space trapezoids... They belong come the "trapezoid" family. Similarly, every rhombi are parallelograms. And all squares are reactangles, are parallelograms, space trapezoids.

See also

Inclusive Definitions: Trapezoids native Dr. Math

Definition of a trapezoid indigenous Wolfram MathworldWolfram Mathworld is very regarded through mathematicians, and their web page presents the typical meaning preferred by them: "A trapezoid is a quadrilateral v two sides parallel." (This is a typical way to native a definition in mathematics, and it way a trapezoid contends least two sides that room parallel, no that the has precisely two sides that hare parallel.)

Inclusive vs exclusive meaning of a trapezoid at Wikipedia

By Maria Miller


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