Question

a
which of the following statements is true only if triangles efi and gfh are similar? (1 point)
$overline{fi} = overline{fh}$
$\frac{overline{gi}}{overline{fi}} = \frac{overline{gh}}{overline{fe}}$
$angle e cong angle g$
segments eg and ih intersect at point f

Explanation:

• The statement $\overline{FI}=\overline{FH}$ is not tied to similarity; it's a congruence of segments that doesn't rely on triangle similarity rules.
• The intersection of segments EG and IH at F is a given in the diagram, true regardless of triangle similarity.
• $\angle E \cong \angle G$ could be true for some non-similar triangles (e.g., vertical angle setups with equal angles but mismatched side ratios).
• For $\triangle EFI \sim \triangle GFH$, the corresponding sides must be in proportion: $\frac{EI}{GH}=\frac{FE}{FG}=\frac{FI}{FH}$. The ratio $\frac{EI}{GH}=\frac{FE}{FG}$ directly reflects the side proportionality requirement that is only guaranteed when the triangles are similar.

Answer:

$\boldsymbol{\frac{EI}{GH}=\frac{FE}{FG}}$