If one wanted to make reference to some seemingly simple mathematical / geometrical definitions, which are globally accepted without ambiguities or differences, which books , institutions or web page should be referenced?
Let me mention how my question started..... It did with at least 2 controversies that arose among my colleagues and students, and we could not elucidate 100% satisfactorily.
1) Does the definition of rhombus include the figures of 4 right angles, then all squares are rhombuses?
2) Are the trapezoids or trapeziums, real parallelograms, or are the parallelograms trapezoids or trapeziums? Or are their definitions mutually exclusive?
This is not a non-euclidean fat triangles derivative composition, or it is not about if you see a colour light green or light light green; or a smell....it is just about plain definitions of very simple and well known geometric shapes. !?
But I am not looking for the definitions now, what I'm really looking for is an unquestionable source of these kind of definitions. I have an answer for both of them that I learned at university, but even in social networks I got into troubles with people when I asked these questions and I gave what I thought was a definition that could not be debated.
I have more examples, but I think these 2 are enough to explain what happens.
Thank you if you have a moment to shed light on my momentary darkness.