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 properties of parallel lines

Parallel lines are two lines that lie in the same plane and do not intersect.

Step2: Analyze each option

• Option A:

Since parallel lines lie in the same plane, if \(\overleftrightarrow{JK}\parallel\overleftrightarrow{LM}\), then \(\overleftrightarrow{JK}\) and \(\overleftrightarrow{LM}\) lie in the same plane.

• Option B:

By the definition of parallel lines, parallel lines do not intersect. So if \(\overleftrightarrow{JK}\parallel\overleftrightarrow{LM}\), \(\overleftrightarrow{JK}\) and \(\overleftrightarrow{LM}\) do not intersect.

• Option C:

Skew lines are non - parallel and non - intersecting lines that do not lie in the same plane. Since \(\overleftrightarrow{JK}\parallel\overleftrightarrow{LM}\), they are not skew.

• Option D:

Perpendicular lines intersect at a right angle. But parallel lines do not intersect, so they cannot be perpendicular.

• Option E:

Parallel lines lie in the same plane, so this option is false.

• Option F:

The symbol \(\parallel\) means parallel. So if \(\overleftrightarrow{JK}\parallel\overleftrightarrow{LM}\), then \(\overleftrightarrow{JK}\) and \(\overleftrightarrow{LM}\) are parallel.

Answer:

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