To compare the lengths of AC to FE using the SSS (Side-Side-Side) Similarity Theorem, we first need to understand that if the triangles are similar, the ratios of their corresponding sides will be equal.
Given that the triangles have corresponding side lengths that satisfy the ratio determined by their similarity transformation (AB/BC = DF/DE), we can directly plug in the values from the sides of the triangles.
To find the ratio of AC to FE, we denote their lengths as follows:
- AC = Length of side AC in the first triangle.
- FE = Length of side FE in the second triangle.
Using the ratios from the Similarity Transformation, we can express the comparison of AC and FE as:
AC / FE = k (where k is the constant of proportionality).
Assuming you have previous calculations that give you the ratio of AC to FE, let's find the right response from the given options, noting they are expressed in fraction form:
- \( \frac{AC}{FE} = \frac{4}{9} \)
- \( \frac{AC}{FE} = \frac{2}{5} \)
- \( \frac{AC}{FE} = \frac{2}{3} \)
- \( \frac{AC}{FE} = \frac{3}{2} \)
To determine the correct ratio, it will depend on the actual lengths of AC and FE based on the provided similar triangles. Depending on the values given (which were not included in your message), you would select the option that reflects the equivalent ratio of the lengths AC and FE.
Since I'm unable to see the image or calculations referenced, please check your side lengths according to the properties of similarity transformation and pick the response that matches your derived ratio of AC and FE.
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