For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

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### Similar Polygons

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- Similar polygons: Two polygons that have the same shape but different sizes; the corresponding sides are proportional

### Similar Polygons

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Similar Polygons 0:05
- Definition of Similar Polygons
- Corresponding Sides are Proportional
- Extra Example 1: Write a Proportion and Find the Value of Similar Triangles 4:26
- Extra Example 2: Write a Proportional to Find the Value of x 7:04
- Extra Example 3: Write a Proportion for the Similar Polygons and Solve 9:04
- Extra Example 4: Word Problem and Similar Polygons 11:03

### Basic Math Online Course

### Transcription: Similar Polygons

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over similar polygons.*0002

*Polygons we know is some kind of shape.*0008

*If we have a triangle, triangles are polygons; squares, rectangles; those are all considered polygons.*0013

*Similar polygons means you have two polygons with the same shape.*0022

*They have to look exactly the same; but they are just different sizes.*0029

*One is going to be smaller or bigger than the other one.*0036

*But then they have to have the same exact shape.*0039

*When they are similar, it is a little symbol like this.*0046

*This means that this triangle here is similar to this triangle here.*0049

*It means that they have the exact same shape.*0054

*It means that one is not going to be any fatter and less taller and all that.*0057

*It is going to have the exact same shape.*0063

*But it is just going to be different sizes.*0066

*An example of similarities, if you are baby.*0072

*You are a baby; you have small hands; you have small feet; you are small.*0079

*As you get older, you grow; but everything has to grow proportionally.*0085

*Your hands grow and your feet grow the same amount.*0090

*If you are a baby and everything is small, as you grow older,*0094

*it is not like only your feet are going to grow but your hands stay the same size.*0100

*Everything has to grow according to how big and small or different let's say size is.*0105

*But then you are still going to have the same shape.*0113

*That is kind of an example of what it means to be similar.*0115

*Everything is proportional when things are similar.*0119

*Again if this is going to grow, if it is going to grow taller, then it also has to grow wider.*0125

*It has to grow in all areas just like a baby grows in all areas.*0130

*Again same shape but different size; then the corresponding sides are proportional.*0137

*Corresponding just means that the side that is basically related to each other.*0144

*This side and this side are called corresponding sides; corresponding sides.*0152

*It means that this side and this side are like the same.*0160

*They are being compared to each other.*0164

*Same thing here; this side with this side and this long side with this long side.*0166

*They are all corresponding.*0171

*That means I can create a ratio for each of these corresponding sides.*0175

*That means I can compare this one with this one.*0182

*4 to 6, remember that is a ratio; then it is all proportional.*0185

*Proportional means that this ratio is going to equal...*0192

*if I make a ratio for this, that is going to be the same.*0195

*For the third side too, this ratio to this is also going to be the same.*0200

*Just saying that all the sides, if you compare this side to this side,*0207

*that ratio is going to be the same as this side to this side.*0211

*It is also going to be the same as this side to this side.*0214

*We have three ratios; we only need two to make a proportion.*0218

*If you have a triangle, you are going to have three different ratios.*0227

*But you only need two.*0229

*You are only going to use the sides that they give you measures for.*0232

*Then you can create a proportion to solve for the missing side.*0238

*See how this all equals each other?--4/6 is equal to 4/6.*0244

*It is also equal to 6/9 because they all equal the same ratio of 2/3.*0251

*All of these ratios equal 2/3; that means these are all the same.*0260

*The first example is these two similar triangles.*0268

*You can draw a little similar symbol like that.*0276

*That means this triangle and this triangle have the same shape but just different size.*0278

*That means I can write a proportion and then find the value of X.*0287

*Here this side is corresponding with this side.*0292

*I can create a ratio comparing this to this.*0300

*The ratio will be 5 to X.*0305

*Again I want to write my ratio as a fraction because that is how I am going to solve my proportion.*0311

*This side to this side is 5 to X.*0316

*That means I can also create a ratio from this side to this side.*0318

*That will be 2 to 4.*0323

*Be careful, if you are going to make a ratio this to this,*0327

*then for the next ratio, the top number has to be from the same triangle.*0333

*If it is going to be this to this, then you have to make the next ratio this to that.*0338

*If you switch it around, then it is not going to be the same.*0343

*It is like saying boys to girls equals girls to boys.*0346

*You are flipping them; you are changing them; you can't do that.*0353

*If it is this triangle to that triangle, then your next ratio has to also be from this triangle to that triangle.*0356

*To solve this, you can use cross products.*0364

*Remember cross products is when you multiply across.*0369

*Or you can just simplify it and then use just mental math.*0372

*Here 2/4, this is the same as 1/2; how do I know?*0378

*2 divided 2 is 1; 4 divided by 2 is 2.*0385

*I can just make this also equal to 1/2.*0390

*1/2, that means the bottom number has to be double the top number.*0397

*5 over what?--what is X going to be?*0401

*If you multiply this by 5, you are going to get 5.*0405

*You have to multiply this by 5; you are going to get 10.*0407

*X has to equal 10; that means this side has a measure of 10.*0412

*Same thing here, we are going to write a proportion to find the value of X.*0425

*Here I can say this to this equal to this side to this side.*0432

*Or if I want, I can start off with this rectangle first as long as I stick to it for my second ratio.*0442

*5, corresponding side is X; 5/X equals... stick with the same one first... 7/14.*0451

*You can write it like that; or you can start with this one first.*0466

*It doesn't matter as long as you stick to that order.*0469

*7/14 is 1/2 because 7 divided by 7 is 1.*0475

*14 divided by 7 is 2.*0484

*That means I need to turn this also into 1/2.*0488

*1 times 5 is 5; 2 times 5 is 10.*0493

*X is going to equal 10.*0503

*If you want to practice cross products, again you are going to just do*0510

*5 times 14 which is going to be equal to X times 7.*0514

*I can write 7 times X.*0524

*You are going to just solve that out and then divide the 7.*0527

*You are going to solve for X that way.*0532

*You are still going to get 10.*0533

*70, 7 times 10 is going to equal 70.*0536

*For the third example, this is called a parallelogram.*0546

*It is not a rectangle because it is not perfectly going straight up and straight across.*0554

*It is not perpendicular; it is kind of tilting off to the side.*0559

*This is a parallelogram; but these are similar polygons.*0564

*Here this is corresponding with this side; this is corresponding with this side.*0572

*But they give you the other sides.*0581

*For a parallelogram, this side and this side are the same.*0584

*I can just write this as 12.*0589

*This side and this side are the same; this is going to be X.*0592

*When I write my proportion, I am just going to do the same thing.*0597

*Ratio of this to this side is 6 to X which is equal to 9 to 12.*0602

*Again I can figure out an equivalent ratio.*0613

*9/12 is the same as... let's divide this by 3; divide this by 3.*0619

*9 divided by 3 is 3/4.*0626

*That means this also has to be the same as 3/4.*0630

*3 times 2 equals 6; that means I have to multiply the 4 times 2.*0638

*X is going to give you 8; that means this side right here is 8.*0645

*Again you can just do cross product; 6 times 12 equals 9 times X.*0652

*Solve it that way.*0660

*For the fourth example, they give us a word problem.*0664

*We have to draw our own similar polygons.*0670

*A tree casts a shadow that is 10 feet long.*0676

*Let's see, I want to draw a tree; there is a tree.*0681

*I know my drawing is kind of bad; there is the ground; tree.*0688

*The shadow... let's say this is a shadow... is 10 feet long; this is 10 feet.*0696

*A person 5 feet tall is standing next to the tree.*0708

*Let's say the person is right here; draw a stick man.*0713

*This is still the same ground.*0720

*Person 5 feet tall is standing next to the tree and is casting a shadow.*0722

*Or let's say this person is 5 feet tall.*0727

*From here down to the ground is 5 feet.*0731

*Where this person is standing, his shadow is 3 feet.*0737

*The triangle formed by the person's height in the shadow...*0747

*That means height and shadow; this is a triangle; you can see that.*0751

*This triangle is similar to the tree and its shadow.*0761

*Then the triangle formed by this tree, here all the way down to this shadow.*0767

*These two triangles, this triangle here and this triangle here, are similar.*0778

*They want us to find... what is it?... the height of the tree.*0785

*How tall is the tree?--I am going to make this X, from here to here.*0796

*Because they said it is similar, I can make a proportion now.*0803

*I can say the 10 feet, the shadow, over the 3 because this side is corresponding to this side.*0808

*It is going to be equal to the tree's height.*0820

*Remember if you started off with this tree triangle, then you have to start it with the next one.*0823

*The tree height X over the person's height, 5.*0830

*From here, now it is a proportion; now I can just solve it out.*0838

*In this case, I can't simplify this.*0845

*I can't do the equivalent fraction method because this is already simplified.*0847

*There is no number that goes into both 10 and 3.*0851

*In this case, I just have to use cross products.*0855

*Here I want to do 3 times X.*0862

*3 times X equals 10 times 5 which is 50.*0865

*Again if I am going to solve for X, I need to divide this 3 because 3 times X is 50.*0874

*It is 50 divided by 3 to find the X.*0880

*If I want to find this, I have to do that.*0887

*Make sure this top number goes inside.*0892

*3 goes into 5 one time; 3, if I subtract it, I get 2; 0.*0895

*3 goes into 20 six times which is 18; I get 2.*0903

*Now that I have a remainder, I have to put my decimal point.*0912

*Bring down another 0; 3 goes into 20 again eight times.*0918

*18 again; 2; another 0; 8.*0926

*It depends on how many numbers after the decimal point your teacher wants.*0934

*But otherwise you can just probably leave it as 16.89.*0940

*Or maybe 16.9 if we are going to round this; round this from that number.*0947

*16.9; that will be in feet.*0954

*The X or the tree is 16.9, almost 17 feet tall.*0961

*Again create your proportion.*0969

*Make sure when you do your ratio, you are going to stick with the same side first.*0970

*It is this side to this side is your ratio.*0976

*Equals this side to that side ratio.*0979

*Then you just solve your proportion using cross products.*0983

*That is it for this lesson; thank you for watching Educator.com.*0988

0 answers

Post by mohamed mansaray on July 17, 2014

I think example four answer on this topic should be 16.66 or 16.7 instead of 16.9. Nonetheless, her lectures are details, just a honest mistake.

0 answers

Post by Magesh Prasanna on May 17, 2013

Ma'm ,In similar polygons You found the ratios of corresponding sides and how did you equate those ratios?

0 answers

Post by Brandon Dorman on February 18, 2013

Hello,

Where can we get more examples and practice problems?

Thanks.

0 answers

Post by Jeanette Akers on October 23, 2012

I've seen problems exactly like example 4 on various standardized tests and never could figure out how to solve them and felt like I was not very bright. Next time I see such a problem on some test, I will know how to solve it. Thanks, Ms. Pyo.

3 answers

Last reply by: Valdo Ribeiro

Sun Dec 11, 2011 4:14 PM

Post by javier mancha on August 19, 2011

she said 3 goes into 20,, 8 times, just like i did, its an honest mistake,

1 answer

Last reply by: Han Jun Kim

Tue Apr 8, 2014 6:36 AM

Post by Nick Socha on July 5, 2011

50 / 3 is 16.6 not 16.8