Is the converse of vertically opposite angles possible?
If the question is whether vertically opposite angles being equal is sufficient to prove that the angles are formed by two intersecting lines (instead of four line segments that terminate at the same point), the answer is: (1) YES, if BOTH pairs of vertically opposite angles are equal. (2) NO, if only ONE pair of vertically opposite angles is known to be equal. The other pair could be inequal, and then “lines” would each be two segments. For example: If the four angles are 89, 90, 91, 90 in order, then 90 is opposite 90, and one pair is equal. But the other pair is not, and while it would probably look like two perpendicular lines, each apparent line would actually be a pair of line segments that met at a 179-degree angle.
