Question

in the diagram, dg = 12, gf = 4, eh = 9, and hf = 3. to prove that △dfe ~ △gfh by the sas similarity theorem, it can be stated that $\frac{df}{gf}=\frac{ef}{hf}$ and
○ ∠dfe is 4 times greater than ∠gfh.
○ ∠fhg is $\frac{1}{4}$ the measure of ∠fed.
○ ∠dfe is congruent to ∠gfh.
○ ∠fhg is congruent to ∠gfh.
○ ∠fhg is congruent to ∠efd.

Explanation:

Step1: Recall SAS similarity

For $\triangle DFE\sim\triangle GFH$ by SAS, we need proportional sides and included - congruent angles.

Step2: Identify included angles

The included angles for the given proportional sides $\frac{DF}{GF}=\frac{EF}{HF}$ are $\angle DFE$ and $\angle GFH$. They must be congruent.

Answer:

$\angle DFE$ is congruent to $\angle GFH$.