Identifying corresponding parts of scaled copies | Geometry | 7th grade | Khan Academy
We are told that figure two is a scaled copy of figure one, and we can verify that by comparing corresponding sides. Corresponding sides are sides that have the same relative position; they're playing the same role in each of the diagrams, even if the diagrams are scaled versions of each other, even if they are different sizes.
So, for example, if we were to compare segment EA right over here, it looks like it corresponds to segment OP. The length of EA is three, while the length of OP is one, two, three, four, five, six. For this to be a scaled copy, the scaling factor from the corresponding side in figure one to the corresponding side in figure two should be a factor of 2. So it’s times 2 right over there.
But let's just answer the questions that they're asking us, and then we can also verify that it is a scaled copy. What point on figure one corresponds to point Q on figure two? All right, pause this video and see if you can figure that out.
All right, so point Q on figure two is right over there. So what point on figure one corresponds to that? Well, it would be playing the same role; it would be in the same relative position. It looks like this point right over here, point B, is in that same relative position. So point B corresponds to point Q on figure two.
Identify the side of figure two that corresponds to segment DC in figure one. Pause this video again and see if you can figure that out.
All right, so segment DC in figure one is that right over there. Your eye might immediately catch that, hey, the segment that's playing the same role in figure two is this one right over here. That is segment NM; put the line over it to make sure that I'm specifying the segment.
We can once again verify the scale factor to ensure that this is a scaled copy. For these two to correspond to each other and for these to be scaled copies of each other, DC has a length of one, two, three, four, and NM has a length of one, two, three, four, five, six, seven, eight. So once again, we are verifying that our scale factor is two.