I ΔABC~ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?

Correct option is A

Given:

ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF

Explanation:

For similar triangles, the corresponding sides are proportional. However, in this case, the triangles are not similar, so the proportionality does not hold.

The following relationships are valid for similar triangles:

​$$\frac{BC}{EF} = \frac{AC}{FD}, \quad \frac{AB}{EF} = \frac{AC}{DE}, \quad \frac{BC}{DE} = \frac{AB}{EF}, \quad \frac{BC}{DE} = \frac{AB}{FD}$$​​

Now, analyzing the given options:

A: BC · EF = AC · FD (This is true for similar triangles, but not necessarily true here)

B: AB · EF = AC · DE (This is true for similar triangles, but not necessarily true here)

C: BC · DE = AB · EF (This is true for similar triangles, but not necessarily true here)

D: BC · DE = AB · FD (This relationship might still hold even if the triangles are not similar)

Thus, the correct answer is:

A: BC · EF = AC · FD