b || f
b || d
c || e
c || d

Question

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", "Corresponding Angles", "Parallel Line Proofs" ], "new_concepts": [], "current_concepts": [ "Linear Pair", "Corresponding Angles", "Parallel Line Proofs" ] } ## Calculate corresponding angles for each line relative to line a $$ \begin{aligned} &\theta_b = 89.5^\circ \quad \text{(top-right angle)} \ &\theta_c = 180^\circ - 91.5^\circ = 88.5^\circ \quad \text{(top-right angle via linear pair)} \ &\theta_d = 180^\circ - 89.5^\circ = 90.5^\circ \quad \text{(top-right angle via linear pair)} \ &\theta_e = 88.5^\circ \quad \text{(top-right angle)} \ &\theta_f = 90.5^\circ \quad \text{(top-right angle)} \end{aligned} $$ ## Identify parallel lines with equal corresponding angles $$ \begin{aligned} &\theta_c = \theta_e = 88.5^\circ \implies c \parallel e \ &\theta_d = \theta_f = 90.5^\circ \implies d \parallel f \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} &b \parallel f \implies 89.5^\circ eq 90.5^\circ \quad (\text{False}) \ &b \parallel d \implies 89.5^\circ eq 90.5^\circ \quad (\text{False}) \ &c \parallel e \implies 88.5^\circ = 88.5^\circ \quad (\text{True}) \ &c \parallel d \implies 88.5^\circ eq 90.5^\circ \quad (\text{False}) \end{aligned} $$

$b \parallel f$

$b \parallel d$

$c \parallel e$

$c \parallel d$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Line Proofs" ] }

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Question

Explanation:

Calculate corresponding angles for each line relative to line a

Identify parallel lines with equal corresponding angles

Evaluate the given options

Answer: