Question

use the law of detachment to determine the valid conclusion, if any, of the following: given: if two lines are coplanar and never intersect, then the lines are parallel. two lines are coplanar and never intersect. conclusion: therefore, — you cannot draw a conclusion the lines are not coplanar and do intersect the lines are not parallel the lines are parallel.

Explanation:

Step1: Recall law of detachment

The law of detachment states that if a conditional statement "if p then q" is true and p is true, then q is true. Here the conditional is "If two lines are coplanar and never intersect, then the lines are parallel" and the given fact is "Two lines are coplanar and never intersect".

Step2: Apply the law

Since the hypothesis (p: two lines are coplanar and never intersect) of the given conditional statement is true, by the law of detachment, the conclusion (q: the lines are parallel) must be true.

Answer:

the lines are parallel.