To determine which two triangles in the figure are similar, let's break down the problem using the given information.

Given:

• $\angle ABC = \angle ADC$

Steps to find the similar triangles:

1. Identify the Triangles:

   • Assume $\triangle ABC$ and $\triangle ADC$ are the two triangles we're considering.

2. Check the Angle Condition:

   • It's given that $\angle ABC = \angle ADC$.
   • Both triangles share a common angle at $\angle A$.

3. Use Angle-Angle (AA) Similarity:

   • For two triangles to be similar, they need to have two corresponding angles equal.
   • In this case:
     • $\angle ABC = \angle ADC$ (given)
     • $\angle BAC$ is common in both triangles.

4. Conclusion:

   • Since two angles in $\triangle ABC$ are equal to two angles in $\triangle ADC$, by the AA criterion, the triangles $\triangle ABC$ and $\triangle ADC$ are similar.

Final Answer:

The two triangles that are similar to each other are $\triangle ABC$ and $\triangle ADC$.

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Would you like more details or have any questions?

Here are some related questions to expand on this concept:

1. What are the criteria for triangle similarity?
2. Can you prove the similarity of triangles using the Side-Angle-Side (SAS) criterion?
3. How does the concept of proportionality work in similar triangles?
4. If the sides of triangle $ABC$ are known, how can you find the sides of triangle $ADC$ given their similarity?
5. Can two triangles be similar if they have one angle equal and the sides around the angle are proportional?
6. What role do parallel lines play in determining triangle similarity?
7. How does the concept of congruence differ from similarity in triangles?
8. Can you derive the length of a side in triangle $ADC$ using the similarity ratio?

Tip: When solving problems involving triangle similarity, always look for corresponding angles and sides to apply the appropriate similarity criterion.