In this activity, line AB, line CF, and line GH have been truncated for ease of exploration.
Assume that line AB is parallel to line CF.
To the left are the angle tools that correspond to ∡ADG and ∡GDB.
Move the angle tools onto the parallel line cut by a transversal to explore relationships between different angles.
Answer the following questions:
1) Are any angles congruent to ∡ADG? Explain why that may occur for each angle.
2) Are any angles congruent to ∡GDB? Explain why that may occur for each angle.
3) Is there any relationship between angles that not congruent? If so, explain.
4) If the only thing you knew about parallel lines was that corresponding angles are congruent, how could we explain that ∡BDG and ∡CEH are also congruent angles?