Question

select the correct answer from each drop - down menu
given: $\angle aob \cong \angle eof$
prove: $\angle boc \cong \angle doe$
(there is a diagram of intersecting lines with points a, b, c, d, e, f around point o)
complete the proof.
suppose that $\angle boc \
ot\cong \angle doe$. by the vertical angles theorem, drop - down menu and drop - down menu. by the transitive property, drop - down menu, and drop - down menu, which contradicts the given. therefore, $\angle boc \cong \angle doe$

Explanation:

Step1: Identify vertical angles

$\angle AOB \cong \angle COD$, $\angle EOF \cong \angle DOE$

Step2: Apply transitive property

If $\angle BOC
cong \angle DOE$, then $\angle AOB
cong \angle EOF$

Step3: Contradict given statement

Given $\angle AOB \cong \angle EOF$, so the assumption is false.

Answer:

1. First dropdown: $\boldsymbol{\angle AOB \cong \angle COD}$
2. Second dropdown: $\boldsymbol{\angle EOF \cong \angle DOE}$
3. Third dropdown: $\boldsymbol{\angle AOB

cong \angle EOF}$