Question

question 10 (multiple choice worth 1 points) which of the following statements is true only if triangles efi and gfh are similar? 2fi = 3fh; (\frac{fh}{fi}=\frac{hg}{ie}); points e, f, and g are collinear; (angle fcongangle f)

Explanation:

Step1: Recall similarity - side - ratio property

For similar triangles, the ratios of corresponding sides are equal. In \(\triangle EFI\) and \(\triangle GFH\), if they are similar, then \(\frac{FH}{FI}=\frac{HG}{IE}\) (corresponding - side ratios).

Step2: Analyze other options

• The equation \(2FI = 3FH\) is a specific ratio that is not a general property of similar triangles. It may or may not be true depending on the scale - factor and is not a necessary condition for similarity.
• The fact that points \(E\), \(F\), and \(G\) being collinear has nothing to do with the similarity of \(\triangle EFI\) and \(\triangle GFH\).
• \(\angle F\cong\angle F\) is always true (reflexive property) and is not a condition that is only true when the two triangles are similar.

Answer:

\(\frac{FH}{FI}=\frac{HG}{IE}\)