Question 1
Given two parallel lines, cut across by a transversal as shown below
When two lines meet , angles are formed. Therefore as the transversal cut the two parallel lines, different angles are formed. To mention but few of these angles are
Corresponding angles
Alternate interior angles
Vertical angles
Alternate exterior angles and so on
From the image in the question, the angles indicated are formed on each of the parallel lines at the same position on the transversal. This angles are shown below
These two angles that form on each of the parallel lines at similar position on the transversal are called corresponding angles and are congruent
Hence, the theorem that proves a is parallel to b (a || b) is the corresponding angle theorem