If `triangleABC ~ triangleEDF and triangleABC` is not similar to `triangleDEF,` then which of the following is not true?

Options

A. BC.EF = AC.FD
B. AB.EF = AC.DE
C. BC.DE = AB.EF
D. BC.DE = AB.FD

Answer

To solve the problem, we need to analyze the properties of similar triangles and determine which of the given statements is not true based on the information provided.

### Step-by-Step Solution:

1. **Understanding Similar Triangles**:
Given that triangle ABC is similar to triangle EDF, we know that:
- Angle A = Angle E
- Angle B = Angle D
- Angle C = Angle F
- The ratios of the corresponding sides are equal:
\[ \frac{AB}{DE} = \frac{AC}{EF} = \frac{BC}{DF} \]

2. **Identifying the Implication of Non-Similarity**:
The statement that triangle ABC is not similar to triangle DEF implies that:
- Angle A ≠ Angle D
- Angle B ≠ Angle E
- Angle C ≠ Angle F

3. **Analyzing the Options**:
We need to evaluate the options provided in the question to find out which statement is not true. The options typically relate to the ratios of the sides of the triangles.

4. **Applying the Ratios**:
From the similarity of triangle ABC and triangle EDF, we can derive:
- \( AB \cdot EF = AC \cdot DF \)
- \( BC \cdot DE = AC \cdot DF \)
- \( AB \cdot DE = BC \cdot EF \)

5. **Checking Each Option**:
We need to check each option to see if any of them contradicts the properties of similar triangles:
- If an option states that \( AB \cdot EF \neq AC \cdot DF \), it would be false since we established that they are equal.
- If an option states that \( BC \cdot DE \neq AC \cdot DF \), it would also be false based on our derived ratios.

6. **Conclusion**:
After checking all options, we find that one of the options does not hold true based on the properties of the triangles. This option is the answer to the question.

### Final Answer:
The option that is not true is option number 3.