Using the vertical angles theorem and the transitive property, we have proven that ∠BOC ≅ ∠DOE as shown below.
Geometry
From the question, we are to prove that ∠BOC ≅ ∠DOE
We are given that
∠AOB ≅ ∠EOF
By vertical angles theorem, we can observe that
∠AOB ≅ ∠DOE and ∠BOC ≅ ∠EOF
Then,
By the transitive property
∠AOB ≅ ∠BOC and ∠EOF ≅ ∠DOE
Therefore, ∠BOC ≅ ∠DOE
Hence, the two angles are equal as proven above.
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