all right what we're going to do in this video is we are going to quickly show how you can tell whether or not a pair of shapes are similar to each other so with this example we have two triangles this triangle has a base of 8 and a height of 12 and this triangle has a base of 6 and a height of 9. now there are a few ways to determine whether or not a pair of shapes are similar to each other one strategy is by comparing all of their corresponding sides for example let's compare the height of this triangle to the height of this triangle now if we took the height of the larger triangle and expressed it as a ratio as compared to the height of the other triangle we can then take this value here and simplify by dividing by the greatest common factor of 3. so we're going to divide 12 by 3 which is equal to 4 and 9 divided by three which is three so we could say that the scale factor between these two triangles would be four to three or we could say it's three to four it depends if you're scaling up or scaling down if you're scaling up then we would say the scale factor is 4 to 3 and if you're scaling down we would say it is 3 to 4. now in order for this to be a similar pair of triangles the same thing has to be true for the corresponding bases of our triangle so let's take 8 and compare it to 6. so we're going to take 8 to 6 and then we're going to simplify this which would be 4 to 3. so not only do the heights have a ratio of four to three but the bases of the triangle do as well so that is one way to confirm whether or not that your shapes are similar and in this case these triangles are similar to each other now another way that we can do this is we could have just set up a proportion we could have taken this height which is 12 and we can compare to this height which is 9 and we want to see if it is equal to the base which is 8 compared to this base which is 6. and we can quickly cross multiply and if we come up with the same product then we know we are dealing with similar figures well 9 times 8 is 72 and 6 times 12 is also 72 so that is another way that you can determine whether or not the shapes are similar to each other now some people just like to use mental math for example like i can look at 9 and compare it to 12 and i know that 9 over 12 would be 3 4. so it's like i'm setting up a fraction in my mind and i'm reducing that fraction to be 3 4. we would say that 9 is part of 12 and 9 out of 12 simplified would be three over four and the same thing for six compared to eight if we were to simplify six over eight mentally we should be able to determine that that is three over four and yet there is one more way we can determine similarity between these two triangles we can take the base of this triangle which is 8 and compare it to the height of the same triangle and the ratio of a triangle's base as compared to its height should be identical to the base compared to the height of the other triangle so 8 compared to 12 should be equivalent to 6 over 9. and if we were to cross multiply we can confirm that that would be true 12 times 6 is 72 and 8 times 9 is also 72 so we would say that these triangles are in fact similar to each other all right let's go ahead and try another example okay we're going to start by writing a ratio of corresponding sides because this side here which is eight centimeters corresponds to this side which is seven centimeters we're gonna write a ratio of eight to seven and we wanna see if that is equal to the ratio of 12 to 10. now notice when i started with this ratio over here i started with the value of 8 which belongs to this rectangle and then the denominator i used a value from the other rectangle so i started with the rectangle on the left on the top or the bigger one and then i went to the smaller one on the bottom so i have to follow the same order when setting up a proportion to check for similarity so we're going to cross multiply here and we have 8 times 10 which is 80 and over here we have 7 times 12 which is 84. so we can see that these rectangles are not similar to each other now just as triangles the height of a rectangle as compared to its base or base compared to height it really doesn't matter in which order you go should be identical to the same comparison of your other rectangle for example 8 as compared to 12 if it were similar to this triangle would be equal to 7 compared to 10. and if we cross multiply you can see that these objects are not similar to each other because we have 80 over here and we have 84 over there so we would say that these shapes are not similar to each other so that is how you can quickly determine whether or not a pair of shapes are similar to each other or not hey i just want to say thanks for checking out my math video please don't forget to hit that subscription button so you can be informed as i upload new math tutorials that just might help you with your math homework until next time this is shane masonette with masonette math 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