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Let's go over each of the questions visible in your image:

### Problem 1–3:
These problems involve determining whether pairs of triangles are **similar**, **not similar**, or if there's **not enough information**. In general, triangles are **similar** if their corresponding angles are equal (angle-angle similarity rule), and the sides are proportional.

1. **Triangle A**: 53°, 71°  
   **Triangle B**: 53°, 71°  
   Since both triangles have two angles in common, they are **similar**.
   
2. **Triangle E**: 63°, 45°  
   **Triangle F**: 14°, 71°  
   These triangles do not have two matching angles, so they are **not similar**.

3. **Triangle G**: 100°  
   **Triangle H**: 70°  
   With only one angle provided, there is **not enough information** to determine similarity.

### Problem 4:
You are asked to draw two equilateral triangles to fit each category in the table: **Not Congruent** and **Not Similar**.  
- **Not Congruent**: Two equilateral triangles that differ in size (but still have all equal sides) would be **similar but not congruent**.
- **Not Similar**: This would be **not possible** because all equilateral triangles are always similar, as they all have the same internal angles (60° each).

### Problem 5:
The question is about whether two equilateral triangles will **always**, **sometimes**, or **never** be similar.
- The answer is **always**. All equilateral triangles are similar because they all have three equal angles (60°) and their sides are proportional.

### Problem 6:
In this figure, it is stated that segment **BC** is parallel to segment **DE**. To show that triangle **ABC** is similar to triangle **ADE**, you can apply the **AA (Angle-Angle) Similarity Criterion**. Since **BC** is parallel to **DE**, angle **A** is shared between both triangles, and corresponding angles at **B** and **D** (and **C** and **E**) are equal. Therefore, the triangles are similar.

Would you like more detailed explanations on any of these problems?

Here are 5 follow-up questions for further practice:
1. What other properties can be used to prove triangles are similar?
2. How can the side lengths of similar triangles help find unknown values?
3. Can two right triangles always be similar? Why or why not?
4. How can you use proportionality to solve problems with similar triangles?
5. What happens to the area of a triangle when all side lengths are doubled?

**Tip:** When determining similarity, focusing on corresponding angles and proportionality of sides can make the problem-solving process easier.

Problems about triangle similarity, equilateral triangles, and parallel lines.

Explore how to determine triangle similarity using the AA Similarity Criterion, draw non-congruent equilateral triangles, and analyze parallel lines in triangle ABC and ADE. These problems cover key concepts such as the AA Similarity Theorem and equilateral triangle properties, suitable for students in Grades 8-10.

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