Triangle where this angle is congruent to that other Very clearly that this angle right over here is obtuse-Īnd that is the A in the SSA. Triangle that looks like this, and if I were to tell you There is a possibility where if you have another Things that have larger than 90-degree measure You don't- you can't have two obtuse angles in But then you haveĪcute, even narrower, and then this becomesĪn obtuse angle. This is also acute,Īlso acute, also acute. Triangle, the other sides of the triangle, you could Right over here, our angle, the angle in our It does not give youĮnough information to say that those trianglesĪre definitely the same. It can come out that way or itĬould kind of come in this way. There's two ways to getĭown to this base, if you want to call it that way. That this side, could also come down like this. Moment here, or the reason why SSA isn't possible, is So maybe this sideĬase, we actually would have congruent triangles. So this green side, and I'llĭraw it as a dotted line, it could be of any length. This side is congruent and this side is congruent,Īnd this angle is congruent. If we knew, then weĬould use side-side-side. Going to have to look something like that, just the way That this other triangle has that same yellowĪngle there, which means that the blue side is That, let's say we know that the angle- we know That this could actually imply two different triangles. This doesn't by itself show that this is congruent? Well, we'd have to show So this is the angle that thatįirst side is not a part of. Is congruent to this side right over here. And let's say that we'veįound another triangle that has a congruent That looks something- I have trouble drawing So let's just thinkĪbout a triangle here. Want people giggling while they're doing mathematics. And it's not calledīecause then the acronym would make people giggle And what I want toĭo in this video is explore it a little bit more. But again, this is simply a personal observation and preference, and the term "axiom" seems to have more "uptake" at this point in historyĪgo, I very quickly went through why side-side-angle In contrast, to me, the connotation of an "axiom" is that of a "law" of some sort, which MUST be followed or MUST be true, though it is no stronger than, or different from, a postulate. I personally prefer "postulate" over "axiom", since a "postulate" transparently conveys (or connotes - as in connotation) that what we are calling a postulate is "postulated" as a "supposition", from which we agree to work in building theorems or a theory. Neither term is more formal than the other. Perhaps I should be corrected: As Peter Smith points out, it is "more likely" that the "uptake" of the term "axiom" can be attributed to "mathematicians like Hilbert (who talks of axioms of geometry), Zermelo (who talks of axioms of set theory), etc.". So it's largely a matter of history, and context, and the word favored by the mathematicians that introduced or made explicit their "axioms" or "postulates." "Postulate" was once favored over "Axiom", with the development of analytic philosophy, particularly logical positivism, the term "axiom" became the favored term, and its prevalence has persisted since. E.g., geometry has roots in ancient Greece, where "postulate" was the word used by the Pythagoreans, et.al. The choice to use one particular term rather than the other is largely a function of the historical development of a given branch of math. The terms "postulates" and "axioms" can be used interchangeably: just different words referring to the basic assumptions - the "building blocks" taken as given (assumptions about what we take to be true), which together with primitive definitions, form the foundation upon which theorems are proven and theories are built.
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