This problem can be transformed into the original problem (asking about 1, 2, or 3) in the following manner:
Divide the shape you are thinking of into triangles by connecting the shape's vertices with lines that only intersect at vertices of the original shape (meaning your new dividing lines can't cross each other). No such lines will be drawn in a triangle (since it's already a triangle), so the number of contained triangles will be 1. For a rectangle, the number of contained triangles will be 2. For a pentagon, the number of contained triangles will be 3. You can then use any of the valid questions from the original problem (referring to the number of contained triangles) to discover the shape. I would rather not spoil the original problem for anyone who still wants to do it, so I won't actually write the question out here.
Let's acknowledge the fact that:
It may be that this is too related to the number of sides (since there is a direct relation between the number of sides of a polygon and the number of triangles which can be drawn within it in the described manner), but technically I didn't use the numbers 3, 4, and 5, so...I only half-cheated.
Here's a goofy solution for fun:
If I open a standard English dictionary at random to an entry in the section of words that begin with the letter 'T' (excluding acronyms), will the first letter of the name of the shape you are thinking of be the same as one of the first two letters of the word I randomly picked?
Here's the explanation to the goofy solution:
If the shape you are thinking of is a Triangle, your answer will be yes, since the word I picked came from the 'T' section in the dictionary, so every word there will begin with 'T'. If the shape you are thinking of is a Rectangle, your answer will be maybe, because I may or may not have picked a word beginning with 'TR'. If your shape is a Pentagon, your answer would be no, because there is no word in a standard English dictionary beginning with 'TP'.