select the correct answer.

given: line segment $\overline{ac}$ and line segment $\overline{bd}$ intersect at o.
prove: $\angle aob \cong \angle cod$

since line segment $\overline{ac}$ and line segment $\overline{bd}$ 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 substitution property of equality, $\angle aob \cong \angle cod$.
by the subtraction property of equality, $\angle aob \cong \angle cod$.
by the congruent complements theorem, $\angle aob \cong \angle cod$.
by the congruent supplements theorem, $\angle aob \cong \angle cod$.

Question

select the correct answer.

given: line segment $\overline{ac}$ and line segment $\overline{bd}$ intersect at o.
prove: $\angle aob \cong \angle cod$

since line segment $\overline{ac}$ and line segment $\overline{bd}$ 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 substitution property of equality, $\angle aob \cong \angle cod$.
by the subtraction property of equality, $\angle aob \cong \angle cod$.
by the congruent complements theorem, $\angle aob \cong \angle cod$.
by the congruent supplements theorem, $\angle aob \cong \angle cod$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Pair Theorem", "Congruent Supplements Theorem" ], "new_concepts": [ "Vertical Angles Theorem" ], "current_concepts": [ "Linear Pair Theorem", "Congruent Supplements Theorem", "Vertical Angles Theorem" ] } ## Identify the given relationships $$ \begin{aligned} &\angle AOB \text{ is supplementary to } \angle BOC \ &\angle BOC \text{ is supplementary to } \angle COD \end{aligned} $$ ## Apply the geometric theorem $$ \begin{aligned} &\angle AOB \text{ and } \angle COD \text{ are both supplementary to the same angle } (\angle BOC) \ &\therefore \angle AOB \cong \angle COD \text{ by the Congruent Supplements Theorem} \end{aligned} $$

By the substitution property of equality, $\angle AOB \cong \angle COD$.

By the subtraction property of equality, $\angle AOB \cong \angle COD$.

By the congruent complements theorem, $\angle AOB \cong \angle COD$.

By the congruent supplements theorem, $\angle AOB \cong \angle COD$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Congruent Supplements Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given relationships

Apply the geometric theorem

Answer: