Which of the following statement is false?

Options

A. All isosceles triangles are similar.
B. All square are similar.
C. All circles are similar
D. None of these

Answer

To determine which of the following statements is false, we will analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement 1:** All isosceles triangles are similar.

- An isosceles triangle has at least two equal sides. However, the angles opposite those equal sides can vary. For example, consider two isosceles triangles with different angles at the vertex. They will not be similar because similarity requires that all corresponding angles are equal. Therefore, this statement is **false**.

### Step 2: Analyze the second statement
**Statement 2:** All squares are similar.

- A square has all four sides equal and all angles equal to 90 degrees. Any two squares, regardless of their size, will have the same shape and the same angle measures. Therefore, this statement is **true**.

### Step 3: Analyze the third statement
**Statement 3:** All circles are similar.

- A circle is defined by its shape, which is constant regardless of the size of the circle. All circles have the same shape and the same angle measures at the center (360 degrees). Therefore, this statement is **true**.

### Step 4: Analyze the fourth statement
**Statement 4:** None of these can happen.

- Since we have already determined that the first statement is false, this statement is not applicable because it suggests that all previous statements are true.

### Conclusion
Based on the analysis, the false statement is **Statement 1: All isosceles triangles are similar**.

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