consider the diagram

given that $r \parallel s$ and $q$ is a transversal, we know that $\angle 3 \cong \angle 6$ by the ______

* corresponding angles theorem
* alternate interior angles theorem
* vertical angles theorem
* alternate exterior angles theorem

Question

consider the diagram

given that $r \parallel s$ and $q$ is a transversal, we know that $\angle 3 \cong \angle 6$ by the ______

* corresponding angles theorem
* alternate interior angles theorem
* vertical angles theorem
* alternate exterior angles theorem

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Alternate Interior Angles Theorem" ], "current_concepts": [ "Alternate Interior Angles Theorem", "Transversal Lines", "Parallel Line Angles" ] } ## Identify the relationship between the given angles $$ \begin{aligned} &\angle 3 \text{ and } \angle 6 \text{ lie between the parallel lines } r \text{ and } s.\ &\angle 3 \text{ and } \angle 6 \text{ lie on opposite sides of the transversal line } q. \end{aligned} $$ ## Match with the geometric theorem $$ \begin{aligned} &\text{Interior angles on opposite sides of a transversal are alternate interior angles.}\ &\text{Since } r \parallel s, \text{ then } \angle 3 \cong \angle 6 \text{ by the alternate interior angles theorem.} \end{aligned} $$

corresponding angles theorem

alternate interior angles theorem

vertical angles theorem

alternate exterior angles theorem

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Alternate Interior Angles Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the relationship between the given angles

Match with the geometric theorem

Answer: