Corresponding points and sides of scaled shapes
About this video
Figure two is a smaller scaled copy of figure one that has also been rotated 180 degrees. The video finds corresponding sides by looking at features like the longest side and right angles: BC matches HL, BA matches LK, and EA matches KJ. Point B corresponds to point L.
You'll be able to
- find corresponding sides in a scaled copy that has been rotated.
- use features such as the longest side and right angles to match parts.
- find corresponding points from corresponding sides.
Key words
- scaled copy
- A copy where every length is multiplied by the same factor.
- corresponding sides
- Sides that play the same role in each figure.
- rotated
- Turned around a point; here, turned 180 degrees (upside down).
- right angle
- A square corner of 90 degrees.
Transcript
- [Instructor] We are told figure two is a scaled copy of figure one. So this is figure two here. This is figure one. Looks like figure two not only has it been scaled down, it's a smaller version, but it also looks like it has been rotated 180 degrees or you can say it's been flipped upside down.
We're asked to identify the side in figure two that corresponds to side EA in figure one. So this is EA in figure one. Pause this video and see if you can identify the side of figure two that corresponds to side EA in figure one. Alright, now let's work through this together.
Some of you might immediately intuit or be able to spot which side corresponds to EA but I'll do it slightly more methodically in this video just so that we can see maybe all of the corresponding sides and points. So one way to think about it is well, it looks like the longest side in figure one is side BC.
So this is the longest side in figure one and then the longest side in figure two is HL so it looks like BC corresponds to HL and then touching on that longest side, that longest side has two right angles. It forms two right angles with the sides next to it. So you have these two right angles right over here and then of those two right angles, you have the shorter side connected to the longest side and so that is BA over here and so that would correspond to LK right over here.
That is the shorter side connected to the long side that forms a right angle and then if we just keep following that side of the shape, we then go to side AE which would correspond now to and this is answering our question to side KJ. So the side in figure two that corresponds to EA in figure one, that is going to be KJ or we could say side JK and if someone wanted to say what points correspond to which point, well, you can see that BA corresponds to LK and BC corresponds to LH so we would know for example that this point B right over here, point B would correspond to point L in figure two right over here and we could use a similar logic for the other points.
So we've answered the questions, the question, but the real thing is to see well, which sides or points have similar features on a relative basis? So I said what is the longest side? What is the longest side? Where do we see right angles? And sometimes your brain might just immediately be able to spot out the shape.
If you were to rotate this one all the way around, it would jump out at you a little bit faster that JK and AE are corresponding sides.
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