So first we want to understand what the question is asking:
What is the relationship between a circumference and a circle that is equivalent to the relationship between a perimeter and a square?
Well, the circumference of a circle measures the distance around the outside of a circle and the perimeter of a square measures the distance around the outside of a square. Oh, so both the circumference and the perimeter are terms that describe similar things for two different shapes (circle and square respectively).
Great, so at a high level, we are looking for a term that defines a property of an object and an equivalent term that defines a similar property for a different object.
So now, let's try to find another pair of geometry terms that does the same thing:
Area, is the same term for all shapes.
Radius/diameter are terms unique to circles, but it's hard to find an analogue for other shapes. Perhaps you can say they are similar to an side in a square, as they can be used to evaluate the area and circumference/perimeter of their shapes.
Triangles have base/height, but once again it's hard to find an exact matching term in another shape.
Well, as we haven't yet found a satisfying match, let's try looking at 3D/solid shapes:
Surface area (total area of the outside of a shape) and volume (total space inside a shape) are the same terms used for all the different shapes.
- Same with edges (line segments that compose a 3D shape) and faces (the flat surfaces that compose a 3D shape).
We still haven't found anything. But wait, if we look back at our goal and the list of geometry terms we've generated, maybe we can find something.
We want to find a pair of terms that describe similar concepts in two different objects. We didn't find anything within 2D objects or 3D objects.
But what if we compare a 2D object to a 3d object? Can we find such a pair of terms?
Reviewing our list, we actually have a ton of these!
Area of a 2D shape (circle) is equivalent to volume of a 3D shape (sphere).
Perimeter of a 2D shape (square) is equivalent to surface area of a 3D shape (cube).
Side of a 2D shape (square) can be equivalent to an edge or a face of a 3D shape (cube). Either the edge or the face can be seen as analogous to the side depending on how you want to define the equivalence in the proportion (I'll leave that for you to think about).
Great, so you can take any of these as answers. Hopefully, using these ideas, you could also come up with any number of additional answers that fit the criteria.
Note: other responses contain trigonometric functions. These could indeed work as well.
What are two terms that define similar properties in different trigonometric function?
Sin(θ) = opposite side / hypotenuse and cos(θ) = adjacent side / hypotenuse.
So another pair of terms could be opposite side is to sine as adjacent side is to cosine (as those sides are two different terms (opposite/adjacent) that define properties of the two different trig functions (sine/cosine) relative to the hypotenuse.