janelle says that lines $l$ and $m$ are skew lines.

is janelle correct?

- yes, because the lines are not parallel
- yes, because the lines will intersect
- no, because the lines are in the same plane
- no, because the lines are perpendicular

Question

janelle says that lines $l$ and $m$ are skew lines.

is janelle correct?

- yes, because the lines are not parallel
- yes, because the lines will intersect
- no, because the lines are in the same plane
- no, because the lines are perpendicular

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Skew Lines" ], "new_concepts": [], "current_concepts": [ "Skew Lines", "Coplanar Lines", "3D Geometry" ] } ## Analyze the definition of skew lines $$ \text{Skew lines} \iff \text{Lines that are not coplanar (do not lie in the same plane) and do not intersect.} $$ ## Examine the given diagram $$ \begin{aligned} &\text{Line } l \text{ lies entirely in the vertical plane } P.\ &\text{Line } m \text{ lies entirely in the horizontal plane } Q.\ &\text{The two planes intersect, but lines } l \text{ and } m \text{ do not lie in a common plane.}\ &\text{The lines are not parallel and do not intersect, meaning they are indeed skew lines.} \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} &\text{Janelle's statement: "Lines } l \text{ and } m \text{ are skew lines" is correct.}\ &\text{Reason: They are not parallel and do not intersect because they lie in different planes.}\ &\text{Option 1: "Yes, because the lines are not parallel" is the correct choice.} \end{aligned} $$

(A) Yes, because the lines are not parallel

(B) Yes, because the lines will intersect

(C) No, because the lines are in the same plane

(D) No, because the lines are perpendicular

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Skew Lines" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the definition of skew lines

Examine the given diagram

Evaluate the given options

Answer: