00:01
Okay, we are going to get into some similarity.
00:03
So first i'm going to explain what? what am i going to explain? the methods in proving similar triangles.
00:09
Okay, so there are, we'll get into this acronym fest over here in a second.
00:18
But proving similar triangles, there is the angle, angle, theorem, the side angle, side, oopsies.
00:35
Let's just write them all out.
00:39
Side, angle, side, and i'm going to add similarity theorem, thm.
00:49
I abbreviate that.
00:51
And then there is side side side similarity similar there at t theorem okay so let's just let's see i'm gonna get some triangles drawn up and then we'll just talk about those for a second hold on okay i in jojo i just made two two triangles and abc is similar to dbe and we're just going to show you how this works.
01:37
So our first one was angle angle if you recall and so for example if you were looking at these two triangles i just put them on top of each other because it's just easier to talk about but abc is its own triangle and and b or db is its own triangle so if we are looking at this we could say well both triangles have angle b and i made de parallel to ac so we could also say that d is congruent to a because of corresponding sides so these two triangles are similar remember similar triangles in a kind of intuitive way have the same shape but different sizes so that's why you're going well that's why when you the angle angle similarity theorem works so nicely is because the angles show that they're the same shape okay and so that's how the angle angle one works let's okay so then there's the the side again we're doing this there's the side angle side one okay so now we need to know before we do this side angle side one we need to know some measures uh let's see uh let's see we're going to measure distance or length um so i'm going to do from here to here and i'm going to go from here to here and then let's do here to here and let's do here to here okay let me get my arrow and move this stuff around a tad okay there's got my arrow we're just gonna move that one down here that's the whole thing that that one's the whole thing.
03:56
Then we'll just move these out a little bit.
03:58
Okay.
04:01
So they both have, let me get my pen.
04:04
Let me get my pen here.
04:06
They both have this angle b in common.
04:09
Both triangles do.
04:10
That's why i chose this side.
04:12
So now what we would need to do to make sure that the sides are proportional is we're going to have two proportions.
04:20
We will have 2 .4 over 4 .8.
04:27
Does this equal 4 .1 over 8 .2? okay, so if you get your calculator out, we're gonna, you could either cross multiply or you could just see if both fractions they come out to be equal i'm just gonna be getting my so 2 .4 i'm just gonna go 2 .4 divided by 4 .8 and i get 0 .5 oh look at that so it's it's a 1 half and then of course 4 .1 divided by 8 point oopsies sorry divided by i know you can't see what i'm doing but just imagine my fingers you're hitting the wrong buttons.
05:14
Basically, if you were to simplify these or cross multiply these, they both simplify down to one half.
05:22
And so, so the ratio of similarity from the big triangle to the small triangle is one half.
05:31
So the small triangle is half the size of the big triangle.
05:34
And since it works for both sides, so this over here were these two sides, and this over here were these two sides and we know that the angle in between those two corresponding sides is okay they have the same angle so those are congruent and the sides are in the same ratio 1 half so each ratio equals 1 half so that is your side angle side that's your side angle side similarity theorem working let us let's do this let's just we're gonna take some of that i'm gonna take just you just get all this writing gone i don't have an erasers or do i i'm missing something i see this i see delete maybe we'll try that try delete there we go yahtzee okay so then for then for oh we need to measure the last one hold on for side side side let me just let me just let me just measure distance okay so i'm gonna go here to here and here to here 7 .9 let's round it off it should be 8 sometimes geogebra it will take like it's 7 .9 9 4 5 6 7 3 4 it's very close to 8 so let's just assume it's 8 so notice that last one if we had 4 over 8 we have another ratio of 1 half so all three sides have the ratio of similarity of 1 half or they're in the ratio of 1 half or they simplify to the ratio of one half so that that would be that one would be side side side okay just a second okay so when we're talking about these two let's just get those up because these are these are interesting to me because having taught college geometry we don't haven't got too far into is this because since we haven't so let's see csstp is corresponding sides similar triangles are they have p shouldn't this be this should be like c no they're proportional sorry it's p are so it shows you i haven't used it very much plus i all these acronyms there's so many acronyms and math and in geometry and the world that i get a little lost so that's that one and the c a stc is the corresponding again correspond angles of similar notice st is similar trying similar triangles are are congruent they're congruent okay so now these real quick these only these are kind of the kind of the reversed thing we're not trying to prove something's similar...