Final answer:
When a transversal crosses parallel lines, several congruent angles and vertical angles are formed, and supplementary angles can occur; whereas complementary angles are not a necessity, and obtuse angles depend on the transversal's orientation.
Step-by-step explanation:
When a transversal crosses parallel lines, several geometrical properties are observed that result in certain types of angles being formed. Let's explore these in detail:
Several congruent angles are formed because when a transversal cuts through parallel lines, corresponding angles are congruent, as are alternate interior angles and alternate exterior angles.
Vertical angles are also formed at the points where the transversal intersects the parallel lines. These vertical angles are always congruent.
Supplementary angles are formed when two angles add up to 180 degrees. This is often true for consecutive interior angles on the same side of the transversal.
However, complementary angles, which add up to 90 degrees, are not necessarily formed when a transversal crosses parallel lines. The formation of obtuse angles is possible depending on the orientation of the transversal.