Final answer:
When segment AD is perpendicular to segment BC, angle BAD is congruent to angle CAD because they are corresponding angles formed by a line intersecting with two parallel lines.
Step-by-step explanation:
When segment AD is perpendicular to segment BC, it forms a right angle at point D. Since angle BAD and angle CAD are both angles formed by a line intersecting with two parallel lines, they are corresponding angles and therefore congruent.