`triangle` ABC with vertices A(0-2,0),B(2,0) and C(0,2) is similar to `triangle` DEF with vertices D(-4,0) ,E(4,0) and F(0,4).

Explanation

To determine whether triangle ABC is similar to triangle DEF, we need to find the lengths of the sides of both triangles and check if the ratios of their corresponding sides are equal.

### Step 1: Find the lengths of the sides of triangle ABC
- **Vertices of triangle ABC**: A(0, -2), B(2, 0), C(0, 2)
- **Length of AB**:
\[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2 - 0)^2 + (0 - (-2))^2} = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]

- **Length of BC**:
\[ BC = \sqrt{(0 - 2)^2 + (2 - 0)^2} = \sqrt{(-2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]

- **Length of AC**:
\[ AC = \sqrt{(0 - 0)^2 + (2 - (-2))^2} = \sqrt{(0)^2 + (4)^2} = \sqrt{16} = 4 \]

### Step 2: Find the lengths of the sides of triangle DEF
- **Vertices of triangle DEF**: D(-4, 0), E(4, 0), F(0, 4)
- **Length of DE**:
\[ DE = \sqrt{(4 - (-4))^2 + (0 - 0)^2} = \sqrt{(4 + 4)^2 + (0)^2} = \sqrt{(8)^2} = 8 \]

- **Length of EF**:
\[ EF = \sqrt{(0 - 4)^2 + (4 - 0)^2} = \sqrt{(-4)^2 + (4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \]

- **Length of DF**:
\[ DF = \sqrt{(0 - (-4))^2 + (4 - 0)^2} = \sqrt{(4)^2 + (4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \]

### Step 3: Calculate the ratios of the corresponding sides
- **Ratio of AB to DE**:
\[ \frac{AB}{DE} = \frac{2\sqrt{2}}{8} = \frac{\sqrt{2}}{4} \]

- **Ratio of BC to EF**:
\[ \frac{BC}{EF} = \frac{2\sqrt{2}}{4\sqrt{2}} = \frac{1}{2} \]

- **Ratio of AC to DF**:
\[ \frac{AC}{DF} = \frac{4}{4\sqrt{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \]

### Step 4: Check if the ratios are equal
- The ratios we calculated are:
- \(\frac{AB}{DE} = \frac{\sqrt{2}}{4}\)
- \(\frac{BC}{EF} = \frac{1}{2}\)
- \(\frac{AC}{DF} = \frac{\sqrt{2}}{2}\)

Since the ratios are not equal, we conclude that triangle ABC is **not similar** to triangle DEF.

### Final Conclusion
The statement that triangle ABC is similar to triangle DEF is **false**.

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