It could be a cone
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the shape that can make two smaller triangles is parallelogram.
The net you are referring to is called a square pyramid net. It consists of four triangular faces and one square base. When the net is folded along its edges and assembled, it forms a three-dimensional square pyramid shape.
Triangular prism
Same size and shape
When you draw a diagonal in a rectangle or a parallelogram, it divides the shape into two congruent triangles, meaning both triangles are the same size and shape. In contrast, drawing a diagonal in a trapezoid results in two triangles that can differ in size and shape, as the bases of the trapezoid are unequal. Thus, different size and shape triangles form only in the trapezoid.