Final answer:
Two parallel lines and a transversal can never form a triangle because parallel lines do not intersect, and hence cannot create the enclosed shape required for a triangle. The correct answer is o never.
Step-by-step explanation:
Two parallel lines and a transversal can never form a triangle. When discussing the characteristics of a triangle, it is essential to consider that a triangle is defined as a three-sided figure lying on a plane, with three interior angles adding up to 180 degrees.
A parallel line is a line in a plane that does not intersect or touch another line in the same plane, no matter how far they extend. A transversal is a line that crosses at least two other lines.
If the lines it crosses are parallel, particular angles are congruent or supplementary. In this case, since there are only two parallel lines and one transversal, they will never meet to form the enclosed shape needed for a triangle.
When two parallel lines are intersected by a transversal, the angles formed on the same side of the transversal and between the parallel lines are called corresponding angles. In a triangle, the sum of the three angles is always 180 degrees. However, corresponding angles formed by a parallel lines and a transversal do not add up to 180 degrees, so they cannot form a triangle.