Given that $\angle ABC = \angle ADC$, we need to find two triangles in the figure that are similar to each other.

Identifying the Similar Triangles

Since $\angle ABC = \angle ADC$, we can look for pairs of triangles that share this angle and another angle or side that would make them similar.

Similar Triangles:

• $\triangle ABC$ and $\triangle ADC$

These triangles are similar because:

1. They share the angle $\angle A$.
2. It is given that $\angle ABC = \angle ADC$.

So, by the AA (Angle-Angle) similarity criterion, $\triangle ABC \sim \triangle ADC$.

Would you like to explore more on this, such as using these similar triangles to solve for unknown side lengths or other properties?

Related Questions:

1. What are the other angles in the triangles $\triangle ABC$ and $\triangle ADC$?
2. How do we apply the AA similarity criterion in geometric problems?
3. Could $\triangle ABC$ and $\triangle ADC$ also be congruent under any conditions?
4. If given side lengths, how would you use the similarity to find unknown lengths?
5. How can the properties of similar triangles be used to solve complex problems?
6. What if a different pair of angles were equal, which triangles might be similar then?
7. How does the proportionality of sides work in similar triangles?
8. How can similarity help in proving other geometric theorems?

Tip: In geometry, always consider whether angles are given, or can be inferred, to help identify similar triangles.