# Square Jordans, Shoes for Nerds

Topic:
Square

## Definition 22

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia. Here we get most of our definitions for quadrilaterals, some are familiar while others not so much. Oblong we call a rectangle today and rhomboid (-oid means "like" and rhombus is "spinning top" so "spinning top-like") we call parallelogram, and trapezia is an old term but it does not mean trapezoid by this definition (literally "table like," guess tables looked different back in the day). Lets work through them: Square: a quadrilateral that has four equal sides and right angles Rectangle: a quadrilateral that has four right angles (think of it as a stretched square) Rhombus: a quadrilateral that has four equal sides (think of it as a skewed square) Parallelogram: a quadrilateral with equal opposite angles and sides (think of it as a skewed rectangle) Trapezoid: a quadrilateral with a pair of parallel sides

## Tool Practice

Use the applet below to drag and drop how you think the shapes will relate to each other in the Venn Diagram below. What does this imply about these shapes? Can a figure be named multiple ways? Could you think of different ways to group these figures?