Identifying corresponding parts of scaled copies
About this video
Figure two is a scaled copy of figure one. The video finds corresponding points and sides (parts in the same relative position) and checks the scale factor: segment ea (3) becomes op (6) and dc (4) becomes nm (8), so the factor is 2.
You'll be able to
- identify corresponding points and sides in scaled copies.
- find a scale factor by comparing corresponding side lengths.
- check that a figure is a scaled copy using more than one pair of sides.
Key words
- corresponding sides
- Sides that are in the same relative position and play the same role in each figure.
- corresponding points
- Points in the same relative position in each figure.
- scale factor
- The number you multiply a length in one figure by to get the matching length in the other.
Transcript
- [Instructor] 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, the same, 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. And the length of ea is three, the length of op is one, two, three, four, five, six. And so for this to be a scaled copy, the scaling factor from, what from the corresponding side in figure one to the corresponding side in figure two, should be a factor of two.
So it's times two right over there. So let's just answer their 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 the 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. And so 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, that is that right over there, and your eye might've immediately catched that hey, the segment that's playing the same role in figure two is this one right over here.
And so that is segment nm. Put the line over it to make sure that I'm specifying the segment. And 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.
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