question 4 of 5
select the correct answer.
given line segment $\overline{ac}$ and line segment $\overline{bd}$ intersect at o.
prove $\angle aob \cong \angle cod$
image of intersecting segments
since line segments $\overline{ac}$ and line segments $\overline{bd}$ intersect at o, $\angle aob$ is supplementary to $\angle boc$ and $\angle boc$ is supplementary to $\angle cod$ by the linear pair theorem.
which statement and reason best completes the proof?
- by the congruent supplements theorem, $\angle aob \cong \angle cod$.
- by the congruent complements theorem, $\angle aob \cong \angle cod$.
- by the substitution property of equality, $\angle aob \cong \angle cod$.
- by the subtraction property of equality, $\angle aob \cong \angle cod$.

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Accepted Answer

# Brief Explanations:
The proof establishes that ∠AOB and ∠COD are both supplementary to the same angle ∠BOC. The congruent supplements theorem states that if two angles are supplementary to the same angle, they are congruent to each other. This matches the logical flow of the proof.
# Answer:
A. By the congruent supplements theorem, ∠AOB ≅ ∠COD.

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