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Added Feb 26, 2019 •

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hello there let's talk about Matt specifically we are right in the middle of chapter 7 talking about congruence and similarity and we've already talked about congruence and what that means in fact this is a little bit of review when you do a translation of a figure the image is congruent to the preimage you have congruence there and with a reflection you also have congruent and with the rotation you also have kangaroo because in all these cases the new image is congruent to the original preimage okay they're the same they're matching but what about when you do a dilation when you do a dime should we don't have congruence anymore now free image any image are similar similar figures are the same shape but different sizes so they're not congruent they're not matching they're not exactly replicas each other each other there's similar same shape different sizes so some other words that kind of go along with that or the ideas of enlarging something or reducing something in other words making it a grow expanded bigger version shrunken smaller version but it has to be to scalar as to be proportional to the original preimage so here's a test is it the same and is it a different size if yes then it is similar like these two shapes are these two shapes similar are they the same shape yeah they're both regular octagons are they the same size no but that's what supposed to be if they're similar so these two shapes are similar because they're the same shape but different sizes okay are these two figures similar yeah they're the same shape of a pentagon but they're different size they're not congruent but they are similar what about these two triangles are these two triangles similar no they're not even the same shape of a triangle ones a right triangle ones an acute triangle these aren't similar they're just two different triangles okay and then yeah these aren't similar to either cuz they're just two different kinds of rectangles they're not like bigger or smaller versions of each other they're not enlargements are reductions of each other does to randomly different rectangles so now these are similar because they're not the same shape okay these two triangles look like they might be similar how can you tell her if they're exact the same shape but we would have to put it to the test to see if they're to scale to see if their proportional so if I look at MN which is 32 and I look at the corresponding part JK which 24 and I make a ratio is that ratio going to be equal to n o which is 20 / k l which is 15 and then the other two corresponding sides which are 24 and 18 when this case if you reduce all of these ratios are fractions you get 4/3 and then you also get 4/3 and then you also get 4/3 again so are these two figures similar yes they're similar because of the same exact shape their proportional they're just different sizes let's try another one these two trapezoids look like they might be similar but the only way to tell is to put it to the test so we're going to do 10 corresponding at 4 and see if that's equal to 5 corresponding to two and then see if that's equal to 20 corresponding to 8 and then see if that's equal to the seven and the three sin we just redo celebes number for reduces to 5/2 5/2 already is in simplest form 20/8 also reduces to 5/2 or looking pretty good except 7 / 3 it's not the same ratio it's not proportional so are these two particular figures similar no those are not similar figures because they're not proportional okay you can also tell if two figures are so if one can be transformed into the other with geometric Transformations like Reflections rotations translations and dilations so if we take triangle EDF and we dilated and then we translate it that gives a similar figures so yes those two triangles are similar because the image was a result of doing geometric transformations to the preimage here's another example are these two rectangles similar kind of hard to tell let's find out we'll take the original and we will rotate it and then we will dilate it and we will translate it yes we have similarity and you can tell because that figure was the result of a series of geometric Transformations that included a dilation which gave us the same shape but a different size that's all we have so see you tomorrow

Uploaded by Jeff Marbut.

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