Determine whether the following sentence is true or false: Any two parallel lines may intersect if they are extended.
For this sentence, I want us to think about what is the definition of parallel lines. Parallel lines are always the same distance apart. These two lines are three units apart. And because they’re parallel at every point, they’re going to be three units apart. No matter how far we extend these lines, they’ll remain three units apart because that is the definition of parallel lines. They do not intersect.
This statement says any two parallel lines may intersect if they are extended. And that is false.