In problem #20, the given information includes:

• $AB = AF$
• $BC = FE$

We are asked to conclude that $CD = DE$.

Explanation:

This problem seems to involve geometric reasoning with triangles or parallel segments. Looking at the diagram and the information given, the triangles formed by $ABC$ and $AFE$ share some congruent parts:

1. AB = AF (given).
2. BC = FE (given).

Since $AB \parallel AF$ and $BC \parallel FE$, these are congruent triangles. The conclusion follows from the fact that corresponding parts of congruent triangles are equal (CPCTC).

Thus, by applying CPCTC, we conclude that $CD = DE$, as they are corresponding parts of the triangles.

Would you like more details or further clarification on any step?

Follow-up Questions:

1. What is CPCTC, and how is it used in congruence proofs?
2. Can you explain how to identify corresponding parts of congruent triangles?
3. What are the other methods to prove two segments are equal in geometry?
4. How do we use parallel lines and transversals to solve geometric problems?
5. What role do congruent triangles play in geometric constructions?

Tip:

In geometry, always look for congruent triangles when two or more sides or angles are given as equal. This can lead you to use properties like CPCTC to conclude equality of other sides or angles.