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The problem is asking if triangles \( \triangle SAM \) and \( \triangle DEL \) are similar, and if so, by which similarity postulate or theorem.

We are provided with:
- Angle \( \angle SAM = 31^\circ \) and \( \angle DEL = 31^\circ \), which shows that these angles are congruent.
- Two pairs of sides: 
  - \( SA = 27 \) and \( DE = 9 \)
  - \( MA = 15 \) and \( EL = 5 \)

To determine the similarity, let's check the **Side-Angle-Side (SAS)** similarity criterion:
- The given angles \( \angle SAM \) and \( \angle DEL \) are congruent.
- The ratios of the corresponding sides:
  \[
  \frac{SA}{DE} = \frac{27}{9} = 3 \quad \text{and} \quad \frac{MA}{EL} = \frac{15}{5} = 3
  \]
  The ratios of the sides are equal, which satisfies the condition for the SAS similarity criterion.

Therefore, the correct answer is **C. Similar - SAS**.

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. What are the criteria for triangle similarity?
2. How does the Angle-Angle (AA) similarity postulate work?
3. Can two triangles with proportional sides but no equal angles be similar?
4. What is the difference between congruence and similarity in triangles?
5. How would you prove similarity using the SSS postulate?

**Tip**: Always look for corresponding angles and side ratios when determining similarity.

Is ∆SAM ~ ∆DEL? If so, identify the similarity postulate or theorem that applies.

Explore how to determine if two triangles are similar using the SAS similarity criterion. This problem examines congruent angles and proportional sides, applying the SAS theorem. Ideal for students in Grades 8-10 studying geometry.

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