Several people have doubted me about the meaning of a trapezoid that shows up in mathematics Mammoth great 5 curriculum:

You can easily find other meanings for a trapezoid which show it only has actually ONE pair of parallel sides. So, civilization get confused.

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

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

Mathematicians like the inclusive definition (the one that claims "at least one pair that parallel lines"). Why? since it provides their theorems shorter to state. If something is true of all trapezoids, the one indigenous "trapezoid" catches all the shapes with at the very least one pair of parallel lines, and also they don"t need to state that it is true because that "trapezoids, parallelograms, rhombi, rectangles, and squares". It simply makes things simpler.

The same is true in the instance of a square matches rectangle. Small children often think in regards to the to exclude, definitions, and view squares as not rectangles. Come them, a rectangle cannot have all equal sides. But, as you most likely know, the inclusive meaning (a rectangle is a form with four sides and four ideal angles) is the prevailing one in the adult world, and also squares are classified as rectangles.

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The reason I provided the inclusive meaning in mathematics Mammoth wasn"t so much because of theorems regarded trapezoids (we don"t really study any in elementary school math). The was since that definition allows united state to attract this neat quadrilateral classification, or tree diagram:


Notice, the trapezoid is presented together ABOVE, or as a "parent" of a parallelogram. In other words, a parallel is a "child" of a trapezoid. It way all parallelograms room trapezoids... They belong to the "trapezoid" family. Similarly, all rhombi room parallelograms. And all squares are reactangles, space parallelograms, room trapezoids.

See also

Inclusive Definitions: Trapezoids from Dr. Math

Definition of a trapezoid indigenous Wolfram MathworldWolfram Mathworld is extremely regarded by mathematicians, and their web page presents the typical an interpretation preferred by them: "A trapezoid is a quadrilateral through two sides parallel." (This is a typical way to indigenous a meaning in mathematics, and it means a trapezoid contends least 2 sides that space parallel, not that the has precisely two sides that hare parallel.)

Inclusive vs exclusive definition of a trapezoid in ~ Wikipedia

By Maria Miller


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