# 10-6 Similar Triangles.mov

today we’re going to be covering ten dash six similar triangles our main idea today is to determine if two triangles are similar and then our second main idea or objective is to use proportions to find unknown lengths of similar triangles okay much of this comes from sixth grade so you may see some things that are familiar to you okay and looking forward you will be seeing this in geometry as well algebra standards would be standard too and also standard one because we are going to be using proportions and properties to calculate okay first thing is vocabulary similar figures now similar figures can also include similar triangles so figures that have the same shape and corresponding angles are congruent and corresponding side lengths are proportional so many of you are probably wondering what corresponding means corresponding means that they are matching okay and congruent means that they are equal you’ll also notice that there is a symbol for similar we use this symbol also known as a till date this symbol to represent similar so you’ll be seeing that frequently throughout the lesson today ok so moving on with that let’s show you a visual on this what does this look like ok so in this diagram I have a statement that says triangle ABC is similar to triangle XYZ ok that’s what this little mark says that’s what the triangles are for so what that really means is that a angle a matches to angle X and you’ll notice that they’re in the same location or both first here so a matches to X B matches to Y so I could say be I’m going to put a double mark on be not just to why ok and then see matches to Z I’m going to put a triple mark to show see just to Z now the reason why we put different markings also is to show that they are different from each other so that means B is not the same as a bee is not the same as C okay so you can see that they’re all different angles okay but they are the same as the corresponding one on the other triangles of matching one okay so let’s do a little bit of matching to get warmed up here two similar triangles okay which angles correspond to each other in other words which ones match in my diagram now you notice angle a matches with angle X so i’m going to right angle by the way this marking is what I use for angle okay it looks like a less than sign but we’re going to put a little angle mark in it so that stands for angle okay angle a is and this is another notation congruent which means they’re equal use a congruent sign angle a is congruent to angle X angle B is congruent to which other angle notice two marks two marks angle why anglesey is the same as angle z so you’ll notice these are the three pairs of matching angles or corresponding angles okay now the next thing in that definition of similar figures the corresponding side lengths have to be proportional which means that matching sides have to form a proportion so let’s take a look which sides match and you can also use the angle marks to help you with that okay so from one mark to two marks we have a to be so a to be matches to one to two marks X to Y and this is proportional which means that the ratio is equal to two to three marks b2c insane oh we’re starting with the same triangle y to z and then finally we’re going all the way around three two one mark c 2 a and C to a would match with Z to X and now we’ve formed a proportion now you’ll notice that this has three ratios okay so this is what we call a proportionality statement and what that means is it just says which ones will be proportional so I can cover up anyone at any time and actually form a proportion I could do these first two and cross multiply this all I could do the last