State, true or false :
All isosceles triangles are similar. 

Answer

To determine whether the statement "All isosceles triangles are similar" is true or false, we can follow these steps:

### Step 1: Understand the definition of isosceles triangles
An isosceles triangle is defined as a triangle that has at least two sides of equal length. Consequently, the angles opposite those equal sides are also equal.

### Step 2: Analyze the properties of isosceles triangles
Since isosceles triangles have two equal sides, they also have two equal angles. However, the third angle can vary, which means that isosceles triangles can have different shapes and sizes.

### Step 3: Draw examples of isosceles triangles
Let's consider two isosceles triangles:
1. Triangle A with angles 60°, 60°, and 60° (an equilateral triangle, which is a special case of isosceles).
2. Triangle B with angles 30°, 30°, and 120°.

Both triangles A and B are isosceles because they have at least two equal sides and two equal angles. However, their angles are different.

### Step 4: Determine if the triangles are similar
For two triangles to be similar, they must have the same shape, which means their corresponding angles must be equal. In our examples, the angles of Triangle A (60°, 60°, 60°) are not equal to the angles of Triangle B (30°, 30°, 120°). Therefore, Triangle A and Triangle B are not similar.

### Conclusion
Since we have found at least two isosceles triangles that are not similar, we can conclude that the statement "All isosceles triangles are similar" is **false**.

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