grade-level dependence of mathematical definitions

In elementary school, a square is not a rectangle, but in higher education it is. In elementary school, a square is not a rhombus, but in higher education it is. In elementary school, a rectangle is not a parallelogram, but in higher education it is. In elementary school a parallelogram is not a trapezoid, but in higher education it is. (In particular, not allowing a rectangle to be a trapezoid would make the statement of the Trapezoidal Rule – which is a really nifty technique of numerical integration in Calculus – rather awkward.) However, on the flip side, in higher education a circle is never considered an ellipse, but in elementary education they seem to use the term ‘oval’ as a catch-all for any convex, smooth, Jordan curve.
keywords: false distinction, false conflation, Mathematics, Geometry