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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallel Lines and Transversals", "Alternate Interior Angles" ], "new_concepts": [ "Triangle Midsegment Theorem", "Consecutive Interior Angles" ], "current_concepts": [ "Triangle Midsegment Theorem", "Parallel Lines and Transversals", "Alternate Interior Angles", "Consecutive Interior Angles" ] } ## Analyze the parallel lines from the given angles $$ \begin{aligned} &\angle ACB = \angle ADE \ &\text{Since } \angle ACB \text{ and } \angle ADE \text{ are corresponding angles for lines } BC \text{ and } DE \text{ cut by transversal } AD: \ &BC \parallel DE \end{aligned} $$ ## Evaluate the first statement $$ \begin{aligned} &BC \parallel DE \ &\angle EBC \text{ and } \angle BED \text{ are consecutive interior angles on the same side of transversal } BE. \ &\angle EBC + \angle BED = 180^\circ \end{aligned} $$ ## Evaluate the second statement $$ \begin{aligned} &\text{The second visible option fragment shows } 2BC = DE. \ &\text{Since } BC \text{ is a midsegment of } \triangle ADE \text{ (connecting the midpoints of } AD \text{ and } AE\text{):} \ &BC = \frac{1}{2}DE \implies 2BC = DE \end{aligned} $$

$\angle EBC + \angle BED = 180^\circ$

$2BC = DE$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Midsegment Theorem" ] }

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Question

Explanation:

Analyze the parallel lines from the given angles

Evaluate the first statement

Evaluate the second statement

Answer: