An old memory - some kid math

Please don't get turned off by the mention of the word 'math' there ... don't worry ... I know my readers :)

Being at home brings back a lot of childhood memories and they are always fun to be talked about. And parents and relatives all around are only too pleased to reiterate them. Anyway, what I intend to bring here is my first mathematical 'discovery', which, to this date, I consider as one of my biggest achievements considering the age at which it came. I thought it had to go somewhere .. so why not here!

I was in class 5 or 6 I guess and so about 10 years old. We were taught congruence of triangles in school. For those who have forgotten this or those who never went to primary school (this is for you, Chandan :D) here is a link providing a description of the 'four' axioms for congruence. http://www.kwiznet.com/p/takeQuiz.php?ChapterID=2817&CurriculumID=24
Please don't take this as an insult if you remember this. This set me into thinking how these axioms guarantee congruence of triangles. This is one thing about that age ... you tend to ask a lot of questions to yourself and to others .. I probably still do .. but that is maybe because I haven't really grown at the same pace as others.

So I was soon fiddling with my compass and pencil trying to figure out a reason for these axioms. I soon figured out the reason, which in itself was an achievement, I think. The reason is of course pretty simple. For example consider the first one on the above link. If two sides and the including angle are given then we can draw the triangle uniquely using pencil and compass. Each of those axioms is based on a similar criterion. However, the fourth axiom (RHS) kind of confused me a little. What was so special about that angle being a right angle. I didn't really understand. While drawing, I tried to alter that angle a little. I soon saw that as soon as you reduce the size of the angle a bit there can be two possible triangles with the given dimensions. This was a good enough justification. But then ... wait!!
It doesn't work for acute angled triangles. But what if we make the size of that angle a little bigger? A little more than 90 degrees. It still works, or so it seemed. And then I drew again ... and then again .. yes, it was working!!!!!
So why restrict this axiom to just the right angle case .. it works for all angles greater than or equal to 90 degrees.

So now, what was the next question in mind? Or rather what were the next questions? Am I the only person to have discovered this? No, it can't be! But then it could be true as well! Most people around are not so smart anyway :D ... I was half imagining myself besides the likes of Srinivas Ramanujan with my picture in the next edition of that Mathematics book. It sounds a little funny now. However, it all just stayed there itself. I couldn't really discuss it with the teacher at school because I was never really liked by math teachers ... too bad this went unpublished until today :D. Probably what I "discovered" is well known by all and was well known even then.

But I still don't understand why that axiom was restricted to right angles in those text-books.