All ………………. Triangles are similar. (isoceles, equilaterial)

Answer

To solve the question "All ………………. Triangles are similar. (isosceles, equilateral)", we need to analyze the properties of isosceles and equilateral triangles.

### Step-by-Step Solution:

1. **Understanding Triangle Types**:
- An **isosceles triangle** has at least two sides that are equal in length and the angles opposite those sides are equal.
- An **equilateral triangle** has all three sides equal in length and all three angles equal (each measuring 60 degrees).

2. **Identifying Similarity**:
- Two triangles are said to be similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion.

3. **Analyzing Isosceles Triangles**:
- In isosceles triangles, while two sides are equal, the third side can vary in length. This means that isosceles triangles can have different shapes and sizes, leading to different angles.
- Therefore, isosceles triangles are not necessarily similar to each other unless they have the same angles.

4. **Analyzing Equilateral Triangles**:
- All equilateral triangles have equal sides and equal angles (60 degrees each). This means that any equilateral triangle can be transformed into another equilateral triangle by scaling (enlarging or reducing) without changing the shape.
- Thus, all equilateral triangles are similar to each other.

5. **Conclusion**:
- Since all equilateral triangles maintain the same angle measures and side ratios, we can conclude that:
- **All equilateral triangles are similar**.

### Final Answer:
All **equilateral** triangles are similar.

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