Question

question 2 of 10
if (overline{jk}paralleloverline{lm}), which of the following statements are true?
check all that apply.
a. (overline{jk}) and (overline{lm}) lie in the same plane.
b. (overline{jk}) and (overline{lm}) do not intersect.
c. (overline{jk}) and (overline{lm}) are skew.
d. (overline{jk}) and (overline{lm}) are perpendicular.
e. (overline{jk}) and (overline{lm}) do not lie in the same plane.
f. (overline{jk}) and (overline{lm}) are parallel.

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are coplanar (lie in the same plane) and do not intersect.

Step2: Analyze each option

• Option A: Since \(\overline{JK}\parallel\overline{LM}\), by the definition of parallel lines, they lie in the same plane.
• Option B: Parallel lines do not intersect.
• Option C: Skew lines are non - coplanar and do not intersect. But \(\overline{JK}\) and \(\overline{LM}\) are parallel (so coplanar), so they are not skew.
• Option D: Perpendicular lines intersect at a right - angle. Parallel lines do not intersect, so they are not perpendicular.
• Option E: Parallel lines are coplanar, so this is false.
• Option F: Given \(\overline{JK}\parallel\overline{LM}\), they are parallel.

Answer:

A. \(\overline{JK}\) and \(\overline{LM}\) lie in the same plane, B. \(\overline{JK}\) and \(\overline{LM}\) do not intersect, F. \(\overline{JK}\) and \(\overline{LM}\) are parallel.