A long-ish wall of text, and I apologize.
Some background: when I was a first-year university student, my chemistry professor was lecturing and was trying to find the word to describe a shape. A student piped up and said, "that's a rhombus." The professor stopped mid-stride, looked at him squarely, and said, "rhombus? That's a stupid word. What's a rhombus? I don't even think that's a word. The word I was thinking of was 'parallelogram'." This was shocking, because this was an American professor, at an American university, and in my American public education, I was taught what a rhombus was in the second or third grade.
Recently, however, I was thinking that maybe my professor wasn't wrong. Consider the naming system for quadrilaterals. The term "quadrilateral" makes some sense: "quad" from Latin for "four", and "lateral" meaning side. And then you get parallelogram, with "parallel" meaning "parallel" and "gram" from Greek meaning "drawn". But then a rectangle is a special case of a parallelogram where the angles are all right angles, which follows clearly enough, and a square is a special case of a rectangle, and important enough to merit its own term.
But then a quadrilateral with only two parallel sides is a trapezoid, which derives from Greek for "table shaped". And then a rhombus is the complement to the square in the special cases of parallelograms -- its angles are anything but right angles!
Confusing yet? We've got the following suffixes describing shapes: -lateral, -gram, -zoid.
We also have triangles, which makes sense because it's "three angles." Yet a "quadrangle" is a region in a university campus.
Increasing the number of sides in the shape, we go from "quadrilaterals" to "pentagons". Ok, now we've gone from the Latin prefix for "four" and a suffix meaning "side" to the Greek for "five" and a totally different suffix. Sometimes we describe the word using a root that means "drawn", and sometimes we describe it by the way that it looks.
And still "rhombus" fits in nowhere in this crazy, convoluted scheme!
To bring this all back to mathematics, and to ask my original question:
Individually, I can find the etymology of each of these terms. But why did the mathematics community adhere to these terms, particularly in elementary education? Did these terms get translated haphazardly from Elements? Is this one of those consequences of the somewhat insular nature of the mathematical community during the Renaissance era? The mathematics community has evolved to be fairly precise in its use of terminology. Why is the terminology surrounding elementary geometry so fragmented?