WEBVTT mathematics/basic-math/pyo
00:00:00.400 --> 00:00:02.000
Welcome back to Educator.com.
00:00:02.000 --> 00:00:08.400
For the next lesson, we are going to go over similar polygons.
00:00:08.400 --> 00:00:13.200
Polygons we know is some kind of shape.
00:00:13.200 --> 00:00:22.000
If we have a triangle, triangles are polygons; squares, rectangles; those are all considered polygons.
00:00:22.000 --> 00:00:29.500
Similar polygons means you have two polygons with the same shape.
00:00:29.500 --> 00:00:36.200
They have to look exactly the same; but they are just different sizes.
00:00:36.200 --> 00:00:39.500
One is going to be smaller or bigger than the other one.
00:00:39.500 --> 00:00:45.900
But then they have to have the same exact shape.
00:00:45.900 --> 00:00:49.500
When they are similar, it is a little symbol like this.
00:00:49.500 --> 00:00:54.100
This means that this triangle here is similar to this triangle here.
00:00:54.100 --> 00:00:56.700
It means that they have the exact same shape.
00:00:56.700 --> 00:01:03.200
It means that one is not going to be any fatter and less taller and all that.
00:01:03.200 --> 00:01:06.300
It is going to have the exact same shape.
00:01:06.300 --> 00:01:12.200
But it is just going to be different sizes.
00:01:12.200 --> 00:01:18.700
An example of similarities, if you are baby.
00:01:18.700 --> 00:01:25.100
You are a baby; you have small hands; you have small feet; you are small.
00:01:25.100 --> 00:01:30.500
As you get older, you grow; but everything has to grow proportionally.
00:01:30.500 --> 00:01:34.300
Your hands grow and your feet grow the same amount.
00:01:34.300 --> 00:01:40.100
If you are a baby and everything is small, as you grow older,
00:01:40.100 --> 00:01:45.300
it is not like only your feet are going to grow but your hands stay the same size.
00:01:45.300 --> 00:01:53.500
Everything has to grow according to how big and small or different let's say size is.
00:01:53.500 --> 00:01:55.500
But then you are still going to have the same shape.
00:01:55.500 --> 00:01:59.300
That is kind of an example of what it means to be similar.
00:01:59.300 --> 00:02:04.700
Everything is proportional when things are similar.
00:02:04.700 --> 00:02:10.100
Again if this is going to grow, if it is going to grow taller, then it also has to grow wider.
00:02:10.100 --> 00:02:17.000
It has to grow in all areas just like a baby grows in all areas.
00:02:17.000 --> 00:02:24.200
Again same shape but different size; then the corresponding sides are proportional.
00:02:24.200 --> 00:02:32.600
Corresponding just means that the side that is basically related to each other.
00:02:32.600 --> 00:02:40.200
This side and this side are called corresponding sides; corresponding sides.
00:02:40.200 --> 00:02:44.100
It means that this side and this side are like the same.
00:02:44.100 --> 00:02:46.300
They are being compared to each other.
00:02:46.300 --> 00:02:51.200
Same thing here; this side with this side and this long side with this long side.
00:02:51.200 --> 00:02:55.100
They are all corresponding.
00:02:55.100 --> 00:03:02.200
That means I can create a ratio for each of these corresponding sides.
00:03:02.200 --> 00:03:05.600
That means I can compare this one with this one.
00:03:05.600 --> 00:03:12.200
4 to 6, remember that is a ratio; then it is all proportional.
00:03:12.200 --> 00:03:15.300
Proportional means that this ratio is going to equal...
00:03:15.300 --> 00:03:20.500
if I make a ratio for this, that is going to be the same.
00:03:20.500 --> 00:03:27.600
For the third side too, this ratio to this is also going to be the same.
00:03:27.600 --> 00:03:31.100
Just saying that all the sides, if you compare this side to this side,
00:03:31.100 --> 00:03:34.400
that ratio is going to be the same as this side to this side.
00:03:34.400 --> 00:03:38.100
It is also going to be the same as this side to this side.
00:03:38.100 --> 00:03:47.000
We have three ratios; we only need two to make a proportion.
00:03:47.000 --> 00:03:49.300
If you have a triangle, you are going to have three different ratios.
00:03:49.300 --> 00:03:51.900
But you only need two.
00:03:51.900 --> 00:03:58.200
You are only going to use the sides that they give you measures for.
00:03:58.200 --> 00:04:04.600
Then you can create a proportion to solve for the missing side.
00:04:04.600 --> 00:04:10.700
See how this all equals each other?--4/6 is equal to 4/6.
00:04:10.700 --> 00:04:20.600
It is also equal to 6/9 because they all equal the same ratio of 2/3.
00:04:20.600 --> 00:04:27.700
All of these ratios equal 2/3; that means these are all the same.
00:04:27.700 --> 00:04:35.800
The first example is these two similar triangles.
00:04:35.800 --> 00:04:38.400
You can draw a little similar symbol like that.
00:04:38.400 --> 00:04:46.700
That means this triangle and this triangle have the same shape but just different size.
00:04:46.700 --> 00:04:52.000
That means I can write a proportion and then find the value of X.
00:04:52.000 --> 00:04:59.800
Here this side is corresponding with this side.
00:04:59.800 --> 00:05:04.900
I can create a ratio comparing this to this.
00:05:04.900 --> 00:05:10.800
The ratio will be 5 to X.
00:05:10.800 --> 00:05:16.300
Again I want to write my ratio as a fraction because that is how I am going to solve my proportion.
00:05:16.300 --> 00:05:18.100
This side to this side is 5 to X.
00:05:18.100 --> 00:05:23.400
That means I can also create a ratio from this side to this side.
00:05:23.400 --> 00:05:27.100
That will be 2 to 4.
00:05:27.100 --> 00:05:32.700
Be careful, if you are going to make a ratio this to this,
00:05:32.700 --> 00:05:37.700
then for the next ratio, the top number has to be from the same triangle.
00:05:37.700 --> 00:05:43.500
If it is going to be this to this, then you have to make the next ratio this to that.
00:05:43.500 --> 00:05:45.700
If you switch it around, then it is not going to be the same.
00:05:45.700 --> 00:05:53.100
It is like saying boys to girls equals girls to boys.
00:05:53.100 --> 00:05:56.600
You are flipping them; you are changing them; you can't do that.
00:05:56.600 --> 00:06:04.600
If it is this triangle to that triangle, then your next ratio has to also be from this triangle to that triangle.
00:06:04.600 --> 00:06:09.100
To solve this, you can use cross products.
00:06:09.100 --> 00:06:12.200
Remember cross products is when you multiply across.
00:06:12.200 --> 00:06:18.000
Or you can just simplify it and then use just mental math.
00:06:18.000 --> 00:06:25.300
Here 2/4, this is the same as 1/2; how do I know?
00:06:25.300 --> 00:06:30.200
2 divided 2 is 1; 4 divided by 2 is 2.
00:06:30.200 --> 00:06:37.600
I can just make this also equal to 1/2.
00:06:37.600 --> 00:06:41.100
1/2, that means the bottom number has to be double the top number.
00:06:41.100 --> 00:06:45.000
5 over what?--what is X going to be?
00:06:45.000 --> 00:06:47.600
If you multiply this by 5, you are going to get 5.
00:06:47.600 --> 00:06:52.500
You have to multiply this by 5; you are going to get 10.
00:06:52.500 --> 00:07:05.600
X has to equal 10; that means this side has a measure of 10.
00:07:05.600 --> 00:07:12.500
Same thing here, we are going to write a proportion to find the value of X.
00:07:12.500 --> 00:07:22.500
Here I can say this to this equal to this side to this side.
00:07:22.500 --> 00:07:31.400
Or if I want, I can start off with this rectangle first as long as I stick to it for my second ratio.
00:07:31.400 --> 00:07:46.100
5, corresponding side is X; 5/X equals... stick with the same one first... 7/14.
00:07:46.100 --> 00:07:48.700
You can write it like that; or you can start with this one first.
00:07:48.700 --> 00:07:54.900
It doesn't matter as long as you stick to that order.
00:07:54.900 --> 00:08:04.200
7/14 is 1/2 because 7 divided by 7 is 1.
00:08:04.200 --> 00:08:07.900
14 divided by 7 is 2.
00:08:07.900 --> 00:08:13.500
That means I need to turn this also into 1/2.
00:08:13.500 --> 00:08:23.600
1 times 5 is 5; 2 times 5 is 10.
00:08:23.600 --> 00:08:29.800
X is going to equal 10.
00:08:29.800 --> 00:08:33.900
If you want to practice cross products, again you are going to just do
00:08:33.900 --> 00:08:44.400
5 times 14 which is going to be equal to X times 7.
00:08:44.400 --> 00:08:47.200
I can write 7 times X.
00:08:47.200 --> 00:08:51.800
You are going to just solve that out and then divide the 7.
00:08:51.800 --> 00:08:52.800
You are going to solve for X that way.
00:08:52.800 --> 00:08:56.500
You are still going to get 10.
00:08:56.500 --> 00:09:05.900
70, 7 times 10 is going to equal 70.
00:09:05.900 --> 00:09:14.100
For the third example, this is called a parallelogram.
00:09:14.100 --> 00:09:19.500
It is not a rectangle because it is not perfectly going straight up and straight across.
00:09:19.500 --> 00:09:24.000
It is not perpendicular; it is kind of tilting off to the side.
00:09:24.000 --> 00:09:31.900
This is a parallelogram; but these are similar polygons.
00:09:31.900 --> 00:09:40.900
Here this is corresponding with this side; this is corresponding with this side.
00:09:40.900 --> 00:09:43.700
But they give you the other sides.
00:09:43.700 --> 00:09:48.700
For a parallelogram, this side and this side are the same.
00:09:48.700 --> 00:09:52.600
I can just write this as 12.
00:09:52.600 --> 00:09:57.000
This side and this side are the same; this is going to be X.
00:09:57.000 --> 00:10:01.900
When I write my proportion, I am just going to do the same thing.
00:10:01.900 --> 00:10:13.100
Ratio of this to this side is 6 to X which is equal to 9 to 12.
00:10:13.100 --> 00:10:19.200
Again I can figure out an equivalent ratio.
00:10:19.200 --> 00:10:25.800
9/12 is the same as... let's divide this by 3; divide this by 3.
00:10:25.800 --> 00:10:29.700
9 divided by 3 is 3/4.
00:10:29.700 --> 00:10:38.300
That means this also has to be the same as 3/4.
00:10:38.300 --> 00:10:45.000
3 times 2 equals 6; that means I have to multiply the 4 times 2.
00:10:45.000 --> 00:10:52.300
X is going to give you 8; that means this side right here is 8.
00:10:52.300 --> 00:10:59.700
Again you can just do cross product; 6 times 12 equals 9 times X.
00:10:59.700 --> 00:11:04.500
Solve it that way.
00:11:04.500 --> 00:11:10.300
For the fourth example, they give us a word problem.
00:11:10.300 --> 00:11:16.400
We have to draw our own similar polygons.
00:11:16.400 --> 00:11:21.000
A tree casts a shadow that is 10 feet long.
00:11:21.000 --> 00:11:28.200
Let's see, I want to draw a tree; there is a tree.
00:11:28.200 --> 00:11:36.100
I know my drawing is kind of bad; there is the ground; tree.
00:11:36.100 --> 00:11:48.400
The shadow... let's say this is a shadow... is 10 feet long; this is 10 feet.
00:11:48.400 --> 00:11:53.100
A person 5 feet tall is standing next to the tree.
00:11:53.100 --> 00:11:59.700
Let's say the person is right here; draw a stick man.
00:11:59.700 --> 00:12:02.300
This is still the same ground.
00:12:02.300 --> 00:12:07.100
Person 5 feet tall is standing next to the tree and is casting a shadow.
00:12:07.100 --> 00:12:10.700
Or let's say this person is 5 feet tall.
00:12:10.700 --> 00:12:17.200
From here down to the ground is 5 feet.
00:12:17.200 --> 00:12:26.800
Where this person is standing, his shadow is 3 feet.
00:12:26.800 --> 00:12:30.900
The triangle formed by the person's height in the shadow...
00:12:30.900 --> 00:12:41.300
That means height and shadow; this is a triangle; you can see that.
00:12:41.300 --> 00:12:47.200
This triangle is similar to the tree and its shadow.
00:12:47.200 --> 00:12:58.000
Then the triangle formed by this tree, here all the way down to this shadow.
00:12:58.000 --> 00:13:05.200
These two triangles, this triangle here and this triangle here, are similar.
00:13:05.200 --> 00:13:16.300
They want us to find... what is it?... the height of the tree.
00:13:16.300 --> 00:13:23.100
How tall is the tree?--I am going to make this X, from here to here.
00:13:23.100 --> 00:13:28.200
Because they said it is similar, I can make a proportion now.
00:13:28.200 --> 00:13:40.000
I can say the 10 feet, the shadow, over the 3 because this side is corresponding to this side.
00:13:40.000 --> 00:13:43.400
It is going to be equal to the tree's height.
00:13:43.400 --> 00:13:50.100
Remember if you started off with this tree triangle, then you have to start it with the next one.
00:13:50.100 --> 00:13:58.300
The tree height X over the person's height, 5.
00:13:58.300 --> 00:14:05.000
From here, now it is a proportion; now I can just solve it out.
00:14:05.000 --> 00:14:06.900
In this case, I can't simplify this.
00:14:06.900 --> 00:14:11.600
I can't do the equivalent fraction method because this is already simplified.
00:14:11.600 --> 00:14:14.800
There is no number that goes into both 10 and 3.
00:14:14.800 --> 00:14:21.800
In this case, I just have to use cross products.
00:14:21.800 --> 00:14:25.400
Here I want to do 3 times X.
00:14:25.400 --> 00:14:33.800
3 times X equals 10 times 5 which is 50.
00:14:33.800 --> 00:14:39.900
Again if I am going to solve for X, I need to divide this 3 because 3 times X is 50.
00:14:39.900 --> 00:14:46.700
It is 50 divided by 3 to find the X.
00:14:46.700 --> 00:14:52.200
If I want to find this, I have to do that.
00:14:52.200 --> 00:14:55.400
Make sure this top number goes inside.
00:14:55.400 --> 00:15:02.900
3 goes into 5 one time; 3, if I subtract it, I get 2; 0.
00:15:02.900 --> 00:15:12.100
3 goes into 20 six times which is 18; I get 2.
00:15:12.100 --> 00:15:17.700
Now that I have a remainder, I have to put my decimal point.
00:15:17.700 --> 00:15:25.900
Bring down another 0; 3 goes into 20 again eight times.
00:15:25.900 --> 00:15:34.100
18 again; 2; another 0; 8.
00:15:34.100 --> 00:15:39.800
It depends on how many numbers after the decimal point your teacher wants.
00:15:39.800 --> 00:15:47.500
But otherwise you can just probably leave it as 16.89.
00:15:47.500 --> 00:15:54.400
Or maybe 16.9 if we are going to round this; round this from that number.
00:15:54.400 --> 00:16:00.800
16.9; that will be in feet.
00:16:00.800 --> 00:16:09.200
The X or the tree is 16.9, almost 17 feet tall.
00:16:09.200 --> 00:16:10.500
Again create your proportion.
00:16:10.500 --> 00:16:15.800
Make sure when you do your ratio, you are going to stick with the same side first.
00:16:15.800 --> 00:16:19.400
It is this side to this side is your ratio.
00:16:19.400 --> 00:16:23.000
Equals this side to that side ratio.
00:16:23.000 --> 00:16:28.000
Then you just solve your proportion using cross products.
00:16:28.000 --> 00:16:31.000
That is it for this lesson; thank you for watching Educator.com.