### Damian Velasquez

Jokes -All squares are rectangles, but not all rectangles are squares.

All squares are rhombuses, but not all rhombuses are squares.

All circles are ellipses, but not all ellipses are circles.

All triangles are triangles :)

All squares are rhombuses, but not all rhombuses are squares.

All circles are ellipses, but not all ellipses are circles.

All triangles are triangles :)

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4 comments

"Typically": There are outliers, but the most common definition is "exactly one", not "at least one".

We could say the same thing about kites and rhombi (that a rhombus is a special kind of kite), but "kite" is usually defined such that rhombi are not kites.

Wolfram MathWorld is an outlier in that it specifically states that a rhombus is a special kind of kite (http://mathworld.wolfram.com/Kite.html), but is non-committal on a parallelogram being a special kind of trapezoid.

Then again, the same can be said of ellipses and circles: A circle is a degenerate ellipse, a rhombus is a degenerate kite, a parallelogram is a degenerate trapezoid.

However, there is one problematic point in allowing parallelograms to be trapezoids: It complicates the definition of "isosceles trapezoid". If parallelograms are not trapezoids, then "isosceles trapezoid" (which is, taxonomically speaking, more interesting than a trapezoid) can be defined as "a trapezoid with one pair of opposite congruent sides", and has the characteristic that the base angles are congruent. If parallelograms are allowed to be trapezoids, then the

We can define terms however we please, but deviating from the standard can create issues elsewhere.

We could say the same thing about kites and rhombi (that a rhombus is a special kind of kite), but "kite" is usually defined such that rhombi are not kites.

Wolfram MathWorld is an outlier in that it specifically states that a rhombus is a special kind of kite (http://mathworld.wolfram.com/Kite.html), but is non-committal on a parallelogram being a special kind of trapezoid.

Then again, the same can be said of ellipses and circles: A circle is a degenerate ellipse, a rhombus is a degenerate kite, a parallelogram is a degenerate trapezoid.

However, there is one problematic point in allowing parallelograms to be trapezoids: It complicates the definition of "isosceles trapezoid". If parallelograms are not trapezoids, then "isosceles trapezoid" (which is, taxonomically speaking, more interesting than a trapezoid) can be defined as "a trapezoid with one pair of opposite congruent sides", and has the characteristic that the base angles are congruent. If parallelograms are allowed to be trapezoids, then the

**definition**of "isosceles trapezoid" has to include "a trapezoid with one pair of opposite congruent sides and two pairs of congruent base angles".We can define terms however we please, but deviating from the standard can create issues elsewhere.

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