 This video is called similar polygons. This video is three slides long and this first slide you actually do not have on your note sheet so feel free to sit back and relax and just watch and listen or if you want to copy some of it down in the margin you certainly can. This is kind of hard because I'm here and you're at home and so when I ask you to think about what the word congruent means to you I don't really have a chance to hear your answer but hopefully if I do ask what does congruent mean to you you can think of basically congruent meaning exactly the same that you can't even read hopefully you think of it as being the same or equal in this case the two stars are exactly the same the sides are all the same length the angles are all the same measure so exactly the same congruent means equal that is the congruent symbol an equal sign with a squiggly above it then asking what does the word similar mean to you a lot of students in the past have said almost the same or looking the same but different and really hopefully you can think of similar as being the same shape different sizes same shape different size this smartboard is really struggling all right I just realigned it hopefully that'll help for the future so similar same shape different size you can see that one star is bigger than the other and all you have to do is if it grew the same amount it would able to end up being identical as the original one or congruent or could end up being bigger or it could even end up being really really small so similar they're the same shape but different sizes and the thing is is that they'd have to um it just has to change in the same amount in all directions so let's keep going so it's kind of asking what two conditions must be satisfied in order to say that two polygons are similar well we have to compare two things we have to compare the angles looks like the smartboard isn't doing too much better and we have to compare the side lengths all right so the thing is is that the angles have to be the same they have to be congruent if you've got two triangles that are similar the angle measures have to be the same it's the side lengths that change because it's when the side lengths grow and shrink that's when the size of the shape changes but the thing is the side lengths have to be proportional that means the side lengths have to change by the same amount all right I was able to make that a little bit neater so just know to prove something similar or not two shapes are similar the angles have to be equal or congruent and the side lengths have to be proportional which means they change by the same amount you're going to be checking something that's called a scale factor you'll learn about that in just a minute let's look at the first example here it asks if the following figures are congruent similar or neither well if you take a look at it let's start with looking at the angles I've got a right angle and a right angle so those match up and then in the bottom left hand corner these are both marked with one arc each that means they're the same even though I don't know how many degrees these angles actually are because they each have one arc I know they represent the same amount and then lastly in the lower right hand corner they both have two arc marks each so this shows that the angles it shows that the angles are equal so now we have to look at the side lengths I notice a three matches up with the three a four matches up with the four and a five matches up with the five so this looks like the side lengths are exactly this so since the angles are congruent and the side lengths are exactly the same we conclude we can conclude that the two figures are in fact congruent they are the exact same shape so we can say they are congruent to each other and this one it kind of makes sense because when you look at the two pictures they do look like they're the exact same triangle and by looking at the angles and looking at the side lengths we confirmed that they are let's try this next one it asks if the following figures are congruent similar or neither well this one I think is fairly obvious because when you look at them they clearly don't look the same the one on the left looks like a parallelogram the one on the right looks like a square so without really doing any work you can rule out the fact that they're congruent then similar remember to be similar they have to be the same shape they're just maybe different sizes these clearly aren't the same same shapes either like we said one's a parallelogram one's a square so I think you could conclude pretty quickly that these shapes are not congruent and they're not similar all right one more example to go now this one's interesting I don't know the names of these shapes they have four sides so I'll call them quadrilaterals and they look like they're the same shape it's just the one on the the left looks a lot bigger than the one on the right so I know automatically that I can't say that the shapes are congruent because they're not the same size they may be the same shape but they're not the same size so what we're going to do is spend some time and see if they're similar to each other so remember so remember we have to look at two things we have to see if the angles are the same and we have to see if the side lengths are proportional let's start with the angles it looks like on the left hand side I have one arc on the left hand side of my small one I have one arc at the tops of each shape there's two arcs each on the right hand side of each shape there's four arcs each and at the bottom of each shape there are three arcs each so we just confirmed that the angles are in fact congruent so now let's take a minute and look at my side length pairs I want to match these up it looks like the six would match with the three the eight would match with the four the ten will match with the five and the twelve will match with the six so we have to figure out if they change by the same amount well let's think about it how do you get from a ten to a five you divide by two how do you get from a five to a ten you multiply by two if all the other side length pairs work in that same way we're going from left to right you divide by two and from going from right to left you multiply by two we will have similar shapes so what I did here I paused it and wrote it because for some reason the smart board works better if I if I write on it while it's paused so take a second and catch up all I did was make fractions or ratios out of my pairings the ten went with the five the six went with the three the eight went with the four and the twelve went with the six these all can simplify down to a two if I wrote them the other way and did five over ten three over six eight over four over eight and six over twelve they would have all simplified to one half so what we just showed here is that all the sides changed by the same amount so we've proven that the side lengths are proportional so therefore these shapes are similar a side note in a future video you're going to be asked to find a scale factor that's what we did here since all the side lengths changed by two two would be our scale factor you'll get that more detail in a video later on tonight