which is enough information to prove that $s \parallel t$?

$\bigcirc$ $\angle 1 \cong \angle 3$
$\bigcirc$ $\angle 2 \cong \angle 8$
$\bigcirc$ $\angle 5 + \angle 6 = 180^{\circ}$
$\bigcirc$ $\angle 1 + \angle 4 = 180^{\circ}$

Question

which is enough information to prove that $s \parallel t$?

$\bigcirc$ $\angle 1 \cong \angle 3$
$\bigcirc$ $\angle 2 \cong \angle 8$
$\bigcirc$ $\angle 5 + \angle 6 = 180^{\circ}$
$\bigcirc$ $\angle 1 + \angle 4 = 180^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Alternate Exterior Angles", "Parallel Line Proofs" ], "new_concepts": [], "current_concepts": [ "Alternate Exterior Angles", "Parallel Line Proofs", "Transversal Lines" ] } ## Analyze the relationship of each option to lines s and t $$ \begin{aligned} &\bullet\ \angle 1 \cong \angle 3 \implies \text{Vertical angles on line } s \text{ (does not relate } s \text{ and } t\text{)} \ &\bullet\ \angle 2 \cong \angle 8 \implies \text{Alternate exterior angles formed by transversal } r \text{ intersecting } s \text{ and } t \ &\bullet\ \angle 5 + \angle 6 = 180^\circ \implies \text{Linear pair on line } t \text{ (does not relate } s \text{ and } t\text{)} \ &\bullet\ \angle 1 + \angle 4 = 180^\circ \implies \text{Linear pair on line } s \text{ (does not relate } s \text{ and } t\text{)} \end{aligned} $$ ## Apply the Converse of the Alternate Exterior Angles Theorem $$ \begin{aligned} &\angle 2 \cong \angle 8 \implies s \parallel t \end{aligned} $$

(A) $\angle 1 \cong \angle 3$

(B) $\angle 2 \cong \angle 8$

(C) $\angle 5 + \angle 6 = 180^\circ$

(D) $\angle 1 + \angle 4 = 180^\circ$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze the relationship of each option to lines s and t

Apply the Converse of the Alternate Exterior Angles Theorem

Answer: