It sounds like you have something less than full aphantasia. Remember it's a spectrum, not a binary.
For me with your triangle example, I know what the equilateral triangle and the parallelogram look like. I could describe them, or draw them, but the whole concept of a mind's eye is completely foreign to me. I don't have any ability to put something in my mind's eye and I guess I conceptually understand what people probably mean by "mind's eye" but I have no experience of it. I conceptually understand things, but there is no imagining happening for me.
A better example might be the brain teasers where you have a cube laid out in 2 dimensions, and you need to fold up that 2 dimensional cube and 'create' a 3d cube and manipulate that 3d cube to solve the brain teaser. From what I understand, most people can do this either completely in their head, or else in their head with some drawing.
The only way I can solve these is to draw the cube with pencil and paper and then use logic while looking at the drawing to figure out the answer. I just have zero ability to in any way create or manipulate a 3d cube in my head. If you took away my pencil and paper I would resort to trying to put together a chain of logic ... "if this side is X, then that side must be Y and the reverse side would be Z" but that quickly becomes confusing and hard to manage.
I also don't experience anything visual when I dream. This is actually how I found out I have aphantasia. I was trying lucid dreaming and none of the instructions made any sense. How am I supposed to fly when I don't have a body in the dream? How am I supposed to flip light switches when there are no light switches?
The cube test is an interesting one, but, to pile on another stupid internet trend, that seems more like a "shape-rotator" vs. "word-cel" question. For very simple fold-ups I can do this, but for more complex decompositions (like if you have me an octahedron) I doubt that I could reliably do this.
In terms of the triangle attaching, is it that without drawing you would not be able even to say what the resulting shape is? If I threw in a third triangle you wouldn't be able to tell me what the shape is now? I'm trying to see if I can get a clear discriminator that tells me whether I am different from you in how I am able to visualize or if we're just using different words (or if I, too, am aphantashic and that other people have powers beyond my ken).
For me with your triangle example, I know what the equilateral triangle and the parallelogram look like. I could describe them, or draw them, but the whole concept of a mind's eye is completely foreign to me. I don't have any ability to put something in my mind's eye and I guess I conceptually understand what people probably mean by "mind's eye" but I have no experience of it. I conceptually understand things, but there is no imagining happening for me.
A better example might be the brain teasers where you have a cube laid out in 2 dimensions, and you need to fold up that 2 dimensional cube and 'create' a 3d cube and manipulate that 3d cube to solve the brain teaser. From what I understand, most people can do this either completely in their head, or else in their head with some drawing.
The only way I can solve these is to draw the cube with pencil and paper and then use logic while looking at the drawing to figure out the answer. I just have zero ability to in any way create or manipulate a 3d cube in my head. If you took away my pencil and paper I would resort to trying to put together a chain of logic ... "if this side is X, then that side must be Y and the reverse side would be Z" but that quickly becomes confusing and hard to manage.
I also don't experience anything visual when I dream. This is actually how I found out I have aphantasia. I was trying lucid dreaming and none of the instructions made any sense. How am I supposed to fly when I don't have a body in the dream? How am I supposed to flip light switches when there are no light switches?