Is the polygon 𝐴𝐵𝐶𝐷 similar to the polygon 𝐸𝐹𝐺𝐻?
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 let’s 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 𝐴𝐵𝐶𝐷 and all side lengths are equal for polygon 𝐸𝐹𝐺𝐻. 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 𝐸𝐹𝐺𝐻, 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.
Let’s also look at the word “corresponding.” It didn’t matter too much in this example because everything was pretty much equal. But if it hadn’t been, it would been really important to understand the corresponding parts.
So notice for the polygons, 𝐴 and 𝐸 were both listed first. So those will be angles that are corresponding and then 𝐵 and 𝐹, 𝐶 and 𝐺, and 𝐷 and 𝐻 and then side lengthwise, 𝐴𝐵 and 𝐸𝐹, 𝐵𝐶 and 𝐹𝐺, 𝐶𝐷 and 𝐺𝐻, and 𝐷𝐴 and 𝐻𝐸.
So as we said it before, these polygons would indeed be similar. So our final answer will be yes.