Corresponding angles in scaled figures

0:00- [Instructor] Triangle ABC is a scaled copy of triangle XYZ. They haven't drawn it for us. Triangle ABC maps to triangle XYZ with a scale factor of one half. Alright, angle A has a measure of 90 degrees. What is the measure of angle X? So pause the video and see if you can figure that out.

0:22Alright, so the key realization here is when you scale a figure, it does not change the angle measures. So you could kind of think of this as a little bit of a trick question. The angle measure of angle X is if it corresponds, if angle X corresponds to angle A in the original triangle, and that's the way that they said it they said triangle ABC maps to triangle XYZ.

0:46So angle X would have the same angle as triangle A doesn't matter that the scale factor is one half. So it'd still be 90 degrees. You might say "Well then what does the scale factor matter?" Well, that would apply to the side lengths. The side, the corresponding side lengths in the second triangle are gonna be one half the length of the corresponding side lengths in the original triangle.

1:05Let's do another example here that touches on some of these issues. So here we are told that figure 2 is a scaled copy of figure 1. They're not drawn to scale. Okay? The question should also say that let's say, let's call it figure R-U-T-S, RUTS, maps onto BEDC, wrap, maps onto B-E-D-C.

1:32I think we have to assume that, that B corresponds to RU corresponds to E and so on and so forth in order to do this. So we have those two things and they say which state two statements must be true about the figures. So the first, actually pause this video have a go at this.

1:48I know it's hard because you might be able to rewind it to look at this and then look back down here. Alright, now let's do this together. The angle of B is equivalent to the measure of angle R. Let's see if that makes sense. So if we made the assumption that I said that, that R-U-T-S maps to B-E-D-C so that R and B correspond to each other and then they will have the same angle, same angle measure.

2:19So I like that one. We can find the measure of angle C by multiplying 107 degrees by the scale factor of two thirds. Let me see, measure of angle C. So they're saying, okay, C corresponds to S. The measure of angle S is 107, but C would have the same angle measure based on what we just said.

2:40It would also be 107 degrees. You wouldn't scale the angle, the scale factor they got from these corresponding sides two to three so it looks like it's a scale factor of two thirds, but it does not affect angle measures. So I do not like choice B, angle T is a right angle, let's see if that makes sense.

2:57Angle T seems to correspond to angle D, and so D is a right angle so T should also be a right angle. So I like that one. And we picked two choices. Let's just hopefully angle E or choice D does not make sense. Angle E is greater than 81 degrees. Let's see. Angle E.

3:16Where are they coming up with this from? Let me scroll properly. So angle E is here. It corresponds to angle U. Angle U has a measure of 81 degrees. They should have the same exact angle measure, so it's not gonna be greater than 81 degrees. So yes, I do not, I do not like that one.

3:33So those are our two choices and we're done.