Question

1. describe a counterexample for each statement below.

a. if two lines are not parallel, then they intersect.
counterexample: ________
hint: what lines are not parallel, but do not
what is intersect?
lines touch, cross

Explanation:

Step1: Understand the statement

The statement is "If two lines are not parallel, then they intersect." We need a counterexample, i.e., two non - parallel lines that do not intersect.

Step2: Recall types of lines in 3D

In three - dimensional space, there are skew lines. Skew lines are lines that are not parallel and do not intersect. For example, consider a line on the ceiling of a room (say, along the length of the ceiling) and a line on the wall (say, along the height of the wall) that is not parallel to the ceiling line. These two lines are not parallel and they do not intersect.

Answer:

Two skew lines in three - dimensional space (e.g., a line on the ceiling and a non - parallel line on the wall of a room) are a counterexample as they are not parallel and do not intersect.