### Video Transcript

Is the polygon ๐ด๐ต๐ถ๐ท similar to the polygon ๐ธ๐น๐บ๐ป?

In order to have similar shapes, we must have two things: their corresponding sides must be proportional and their corresponding angles must be equal. So letโs first begin by deciding if their corresponding sides are proportional, meaning does the relationship between the sides stay the same?

So if one shape has a side length that is twice as long as the other shape, then it must be that every side length of the larger figure must be twice as long. And the important piece here is that all side lengths are equal for polygon ๐ด๐ต๐ถ๐ท and all side lengths are equal for polygon ๐ธ๐น๐บ๐ป. So however one pair of sides that are corresponding are related, it must be the same for them all. Therefore, their corresponding sides would indeed be proportional.

Just to make an example, say these side lengths were two and then for a polygon ๐ธ๐น๐บ๐ป, those side lengths were twice as large, making this one four, this one four, and these four. It stay proportional.

Now, are their corresponding angles equal? They must be because every single angle is equal to 90 degrees. So all of the angles are equal. So since they have equal side lengths and each angle is 90 degrees, these must be squares.

Letโs also look at the word โcorresponding.โ It didnโt matter too much in this example because everything was pretty much equal. But if it hadnโt been, it would been really important to understand the corresponding parts.

So notice for the polygons, ๐ด and ๐ธ were both listed first. So those will be angles that are corresponding and then ๐ต and ๐น, ๐ถ and ๐บ, and ๐ท and ๐ป and then side lengthwise, ๐ด๐ต and ๐ธ๐น, ๐ต๐ถ and ๐น๐บ, ๐ถ๐ท and ๐บ๐ป, and ๐ท๐ด and ๐ป๐ธ.

So as we said it before, these polygons would indeed be similar. So our final answer will be yes.