Question

the ratios of corresponding sides in the two triangles are equal.
what other information is needed to prove that △fge ~ △ijh by the sas similarity theorem?
○ ∠f ≅ ∠j
○ ∠i ≅ ∠f
○ ∠e ≅ ∠h
○ ∠g ≅ ∠i

Explanation:

Step1: Identify side ratios

For $\triangle FGE$ and $\triangle IJH$, compute side ratios: $\frac{FG}{IJ}=\frac{15}{10}=\frac{3}{2}$, $\frac{FE}{IH}=\frac{30}{20}=\frac{3}{2}$.

Step2: Apply SAS similarity

SAS similarity needs equal included angles. Included angles for the ratios are $\angle F$ (between $FG, FE$) and $\angle I$ (between $IJ, IH$).

Answer:

B. $\angle I \cong \angle F$