When you have two straight lines in the plane, there are two alternatives: 1. These two straight lines intersect (as shown in Figure 1a), and 2. These two straight lines do not intersect even at extended length (as shown in Figure 1b). |
Figure 1a. Intersecting straight lines |
Figure 1b. Parallel straight lines |
Definition Two straight lines in a plane are called parallel if they do not intersect even at extended length. The next statement is a postulate, that is a statement, which is accepted without proof: For a given straight line and a point in the plane outside of this straight line there is |
Figure 2. The unique parallel straight line passing through the given point out the line |