This question is asking whether triangles $\triangle ABC$ and $\triangle DEF$ are similar, and if so, which similarity postulate applies.

We are given:

• $\angle A \cong \angle D$
• $\angle B \cong \angle E$
• $AB = 4$ and $DE = 8$

To determine similarity, let's go over the similarity postulates:

1. AA (Angle-Angle) Similarity: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
2. SAS (Side-Angle-Side) Similarity: If two sides of two triangles are proportional and the included angle is congruent, the triangles are similar.
3. SSS (Side-Side-Side) Similarity: If all three corresponding sides of two triangles are proportional, the triangles are similar.

In this case:

• We know $\angle A \cong \angle D$ and $\angle B \cong \angle E$, which fulfills the AA condition.
• There is no need to check side proportions, as the AA similarity theorem is sufficient.

Thus, the correct answer is: C. Similar - AA

Would you like more details or have any other questions?

Here are 5 related questions to explore:

1. What other similarity theorems exist besides AA, SAS, and SSS?
2. How do you use the SAS similarity postulate in problems involving proportions?
3. What is the significance of triangle similarity in geometry?
4. Can two triangles be similar if only one pair of angles is congruent?
5. How do you determine whether two triangles are congruent rather than similar?

Tip: Always verify whether you have enough information to apply a similarity postulate before making a conclusion.