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A triangle, in standard 2 dimensions cannot have any parallel sides.

Let's show without going into formal proof.

Let's say that you try to make a triangle with 2 parallel sides.

-------------side a-------------

|C

|

|

|side b

|

|

|A

-------------side c---------------

Side a & b intersect at vertex C. Side b & c intersect at vertex A,

and since sides a & c are parallel, they will never intersect, so there is no

third vertex, so it's not a polygon, much less a triangle.

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