Sequences of Transformations. HL Hypotenuse-Leg Congruence. Sum of Exterior Angles. View All Related Lessons. The answer is no. Here is a video demonstrating why with an example.
Show Solution Check. You've reached the end. These two triangles must be exactly identical so the two shortcuts that don't work angle angle angle because we'll create two triangles that'll have different sizes although they're will have same angles and the second one that doesn't work is the side side angle not only because it's a [IB] but also because we create two different triangles.
All Geometry videos Unit Triangles. Previous Unit Constructions. Next Unit Polygons. Brian McCall. Thank you for watching the video. Start Your Free Trial Learn more. Brian McCall Univ. Geometry Triangles. Well, we'd have to show that this could actually imply two different triangles. And to think about that, let's say we know that the angle-- we know that this other triangle has that same yellow angle there, which means that the blue side is going to have to look something like that, just the way we drew it over here.
This side down here, I'll make it a green side. This green side down here we know nothing about. We never said that this is congruent to anything. If we knew, then we could use side-side-side. We only know that this side is congruent and this side is congruent, and this angle is congruent.
So this green side, and I'll draw it as a dotted line, it could be of any length. We don't know what the length is of that green side.
Now we have this magenta side. We have another side that is congruent here. So this thing could pivot over here. We know nothing about this angle so it could form any angle. But it does have to get to this other side. So one possibility is that maybe the triangles are congruent. So maybe this side does go down just like that, in which case, we actually would have congruent triangles.
But the kind of aha moment here, or the reason why SSA isn't possible, is that this side, could also come down like this. There's two ways to get down to this base, if you want to call it that way. It can come out that way or it could kind of come in this way. And so that's why SSA by itself with no other information is ambiguous. It does not give you enough information to say that those triangles are definitely the same.
Now there are special cases. So in this situation right over here, our angle, the angle in our SSA, our angle was acute. This is an acute angle right over here. And when you have an acute angle as one of the sides of your triangle, the other sides of the triangle, you could still have an obtuse angle. Remember, acute means less than 90 degrees, obtuse means greater than 90 degrees. So you could still have an obtuse angle. So that's why this is an option.
So one option is that you have two other acute angles. So this could be acute. This is also acute, also acute, also acute. But then you have the option where this is even more acute, even narrower, and then this becomes an obtuse angle. And that's only possible if you don't-- you can't have two obtuse angles in the same triangle. You can't have two things that have larger than degree measure in the same triangle.
And so that's why there is a possibility where if you have another triangle that looks like this, and if I were to tell you very clearly that this angle right over here is obtuse-- and that is the A in the SSA.
0コメント