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3. choose the correct answer. which lines are concurrent? \\( \\overlef…

Question

  1. choose the correct answer.

which lines are concurrent?
\\( \overleftrightarrow { m q } \\) and \\( \overleftrightarrow { p t } \\)
\\( \overleftrightarrow { r s } \\) and \\( \overleftrightarrow { p t } \\)
\\( \overleftrightarrow { r s } \\) and \\( \overleftrightarrow { o s } \\)
\\( \overleftrightarrow { r s } \\) and \\( \overleftrightarrow { m q } \\)

Explanation:

Step1: Recall the definition of concurrent lines

Concurrent lines are lines that pass through the same point.

Step2: Analyze each option

  • For \(\overleftrightarrow{MQ}\) and \(\overleftrightarrow{PT}\): These lines are parallel (since \(MQ\perp QA\) and \(PT\perp PA\) and \(QA\parallel PA\) in the cube - like structure), so they do not intersect.
  • For \(\overleftrightarrow{RS}\) and \(\overleftrightarrow{PT}\): These lines are skew (not parallel and not intersecting in 3 - D space).
  • For \(\overleftrightarrow{RS}\) and \(\overleftrightarrow{OS}\): These lines intersect at point \(S\).
  • For \(\overleftrightarrow{RS}\) and \(\overleftrightarrow{MQ}\): These lines are parallel (since \(MQ\) and \(RS\) are both perpendicular to the vertical edges of the cube - like structure in their respective planes).

Answer:

\(\overleftrightarrow{RS}\) and \(\overleftrightarrow{OS}\)