If line JK is parallel to line LM, which of the following statements are true? A. JK and LM are perpendicular. B. JK and LM lie in the same plane. C. JK and LM do not lie in the same plane. D. JK and LM are skew. E. JK and LM are parallel. F. JK and LM do not intersect.

The true statements are: B, E, and F.

Explanation

  • E (JK and LM are parallel) — True by the given information.
  • B (JK and LM lie in the same plane) — True: by definition, parallel lines are coplanar (they lie in the same plane).
  • F (JK and LM do not intersect) — True under the standard school definition of parallel lines: two distinct parallel lines in the same plane never meet.

Why the others are false:

  • A (perpendicular) — False: perpendicular lines meet at a right angle; parallel lines do not meet, so they cannot be perpendicular.
  • C (do not lie in the same plane) — False: that contradicts the coplanar nature of parallel lines.
  • D (skew) — False: skew lines are non-coplanar and non-intersecting; parallel lines are coplanar, so they cannot be skew.

Note: If your course uses a broader definition that allows “parallel” to include the same line (coincident), then F would be false in the coincident case (they would intersect at every point). In most textbook/contest settings, “parallel” means distinct, nonintersecting coplanar lines, so B, E, and F are the intended true statements.

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