One thorn in the side of geometry teachers is difficulty untangling the relationship between squares, rectangles, rhombuses, and parallelograms. I’ve seen it done with flow charts and I’ve seen in done with Venn diagrams, but neither fully satisfied what I wanted. So I combined the two:
Here’s a version with trapezoids and kites:
Filed under: Education, Mathematics, Visual Design |
The Number Warrior 
where’s your kites and trapezoids?
Kites are like monkey wrenches, except they fly.
Jonathan
Got ’em too. (Although the four I mentioned are the main source of pain.) Will add shortly.
EDIT: There you go. I also tossed in a arrow between “square” and “parallelogram”.
So American….
In ABCD, AB = BC and CD = DA, and it might be a kite?
In EFGH, EF || HG, and it might be a trapezoid.
I am convinced that we use these exclusive definitions just to make that diagram work!
It bothered me as a kid, and really still does, lengthen the short base of a trapezoid, continuously, and at one moment it stops being a trapezoid, and the next it starts again.
For my version, I think I’d want a single “k” and a single “t” in the center to represent the one case of each which also meets the definitions of square, etc.
I am using the definitions from our state test.
Jeff Miller mentions the trapezoid and differing Geometry books: http://jeff560.tripod.com/ambiguities.html
The kite also is apparently ambiguous.
If you want to cover those cases you can just add arrows, although I’d also rearrange things to be clearer.
Depending on the textbook, trapezoids are defined as having exactly one pair of parallel sides OR at least one pair of parallel sides. In the second case, parallelograms, rectangles and squares can be considered trapezoids. As for kites, the definition states that there are two distinct pairs of consecutive sides that are congruent. We do a flowchart diagram with kite and trapezoid at the top flowing down to the other shapes.