Comparing triangles by analyzing angle and side arrangements

0:00- [Instructor] Consider the following triangles. Which statements about the triangles are true? And they want us to pick two answers, so pause the video and try this on your own. Okay so the first statement, the triangles are identical copies of each other. See, is that the case?

0:17Well, it looks like this side that is of length five that is between the 63 degree angle and the 60 degree angle in both of these triangles. Or another way to think about it, that side of length five is adjacent to both of those angles. So, so far that's looking pretty good.

0:36But then when I look at the other side, the side of length eight, the side of length eight right over here, in the first triangle, it is opposite the 63 degree angle. And then in this second triangle, it's not opposite the 63 degree angle, it's opposite the 60 degree angle.

0:57So I don't think these are identical copies of each other. So I'm going to rule this one out. The side, let me go back to, well, I'll use blue. The side labeled five is adjacent to the 63 degree angle in both triangles. Yeah, that's right. Here's the 63 degree angle, five is adjacent to it.

1:1663 degree angle, five is adjacent to it. So I like this choice. I need to find one more now. The triangles cannot be the same because they have different orientations. No, you can definitely rotate things around and still say that these triangles are the same.

1:33I guess it depends on how you define same. But usually in geometry you'll say that these triangles will, in the future we'll use words like congruent, et cetera, but you can reorient themselves and they're still the same. So I do not like that choice. So let's hope that D, let's hope that D actually works.

1:51The 63 degree angle is between different sides in each triangle. So here it's between five and whatever this side is. And it's not the eight length. In fact, we know that this isn't going to be eight here, because this is a different angle here. I don't want to get too much into it, but we know this isn't an isosceles triangle 'cause we have different angles here and then we can even calculate that this angle, this angle's gonna be 57 degrees over here, 57 degrees over here.

2:21So we're not going to have a situation where any of these sides are the same. So we know that this side is, let's put it this way, it is not eight or five. And this one right over here, this one right over here is not eight or five either. Not eight or five. They're not necessarily going to be the same, but they're definitely not eight or five.

2:46So the 63 degree angle is between different sides in each? Yes it's here, the 63 degree angle is between the five side and the not eight or five side. While here, the 63 degree angle is between the five side and the eight side. So it's between different sides in each triangle.

3:03So I like choice D, as well.