https://file.aiquickdraw.com/mathbot/file/1726758584283gti4ayp6.jpg

In the image provided, you are asked to determine if \(\triangle ABC \sim \triangle DEF\) and, if so, identify the similarity postulate or theorem that applies.

### Key Information from the Diagram:
- Both triangles have angles marked \(30^\circ\) and \(85^\circ\).
- The remaining angle in both triangles must be \(180^\circ - (85^\circ + 30^\circ) = 65^\circ\) since the sum of the angles in any triangle is always \(180^\circ\).

### Conclusion:
Since two corresponding angles in \(\triangle ABC\) and \(\triangle DEF\) are congruent, by the **Angle-Angle (AA) Similarity Postulate**, the triangles are similar.

### Correct Answer: 
**A. Similar - AA**

Would you like further details or have any questions about this? Here are some related questions for deeper understanding:

1. What is the Angle-Angle (AA) Similarity Postulate?
2. Can you explain how to verify similarity using the Side-Side-Side (SSS) theorem?
3. How does the Side-Angle-Side (SAS) theorem establish triangle similarity?
4. Why is the sum of the angles in any triangle always \(180^\circ\)?
5. How do you prove two triangles are congruent instead of just similar?

**Tip:** Always check if two triangles have at least two equal angles to quickly apply the AA similarity postulate.

Is △ABC ~ △DEF? If so, identify the similarity postulate or theorem that applies. The given angles are 30°, 85°, and the third angle can be calculated as 65° for both triangles.

Determine if △ABC ~ △DEF using the Angle-Angle (AA) similarity postulate. Both triangles share two congruent angles, making them similar. This problem covers key geometry concepts, including triangle angle sums and the AA similarity postulate, suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation