We're using Pearson's Geometry in my class.

As terms are defined there, Parallelograms include Rhombi (congruent sides), Rectangles (right angles), Squares (congruent sides and right angles, i.e. Rhombi that are Rectangles), and of course Parallelograms that are neither Rhombi nor Rectangles. Non-Parallelograms include Kites (consecutive sides congruent but opposite sides never congruent) and Trapezoids (exactly one pair of parallel sides), and again, Non-Parallelograms that are neither Kites nor Trapezoids.

I wonder. What's the point of defining the Non-Parallelograms that way? No Trapezoid property depends on the fact that some opposite sides are not parallel, and no Kite property depends on the fact that opposite sides are not congruent. It seems to me it would be more interesting and more natural to drop those requirements and to say that Trapezoids are quadrilaterals with at least one pair of opposite sides parallel (so that all Parallelograms are Trapezoids) and Kites are quadrilaterals in which each side is congruent to at least one consecutive side (so that all Rhombi are Kites).

What's the point in the lopsided way of defining terms, so that some categories intersect and some are disjoint?



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