- [Instructor] What we're going to do in this video
is look at pairs of figures,
and see if they are scaled copies of each other.
For example, in this diagram,
is Figure B a scaled version of Figure A?
Pause the video and see if you can figure that out.
There's multiple ways that you could approach this.
One way is to say,
"Well, let's see what the scaling factor would be."
We could look at the side lengths.
This side right over here has length three on Figure A.
This side length right over here
has length one, two, three, four, five.
This side length has length five as well.
This has length five.
This length, we could figure it out
with the Pythagorean Theorem,
but I won't even look at that one just yet.
But let's look at corresponding sides.
To go from this side.
If we scale up, the corresponding side to that
would be this side right over here.
What is its length?
Well, its length, when you scale it up, looks like five.
So to go from three to five
you would have to multiply by 5/3.
5/3.
But let's look at this side now.
It's five in Figure A.
What length is it in Figure B?
Well, it is one, two, three, four, five.
It's still five, so to go from five to five,
you have to multiply it by one,
and so you have a different scaling factor
for corresponding,
or what could have been corresponding sides.
This side right over here, you're scaling up by 5/3,
while this bottom side, this base right here,
you're not scaling at all.
So these actually are not scaled versions of each other.
Let's do another example.
In this example, is Figure B a scaled version of Figure A?
Pause the video and see if you can figure it out.
All right, well we're gonna do the same exercise,
and here they've given us
the measures of the different sides.
This side has length two.
This side has length
the corresponding side,
or what could be the corresponding side has length six.
To go from two to six, you have to multiply by three.
If we look at these two potentially corresponding sides,
that side and that side, once again,
to go from four to twelve, you would multiply by three,
so that is looking good as well.
Now to go from this side down here, this has length six.
The potentially corresponding side right over here
has the length 14.
Well here we're not multiplying by three.
If these were scaled
If Figure B was a scaled-up version of Figure A,
we would multiply by three,
but six times three is not 14, it's 18,
so these actually are not
Figure B is not a scaled version of Figure A.
Let's do one more example.
Once again, pause this video
and see if Figure B is a scaled version of Figure A.
We're gonna do the same exercise.
Let's look at potentially corresponding sides.
That side to that side,
to go from four to 12,
we would multiply by three,
and then we could look at this side and this side,
to go from four to 12, once again you multiply by three,
so that's looking good so far.
We could look at this side and this side,
potentially corresponding sides.
Once again, we're going from four to 12,
multiplying by three.
Looks good so far.
And then we could look at this side and this side.
2.2 to 6.6, once again multiplying by three.
Looking really good.
And then we only have one last one to check.
2.2 to 6.6, once again multiplying by three,
so all of the side lengths have been scaled up by three,
so we can feel pretty good that
Figure B is indeed a scaled-up representation of Figure A.