# parallel lines

Fig 1. Parallels to a line.

**Parallel lines** are two or more lines that lie in the same plane and never intersect each other. They are equidistant from each other and have the same slope.

1. To construct a straight line *m* through a given point, parallel to a straight line *I*. Draw through the given point P an arbitrary straight line *l*_{1} intersecting *l* in the point *A*. *I* and *l*_{1}, form together the angle α (Fig 1 left). At *P* on *l*_{1} lay out the angle α, on the same side of *A*, and in the same sense, from *AP*. Then the free arm of the new angle gives the direction of the required parallel m. *l*_{1} may conveniently be chosen to be perpendicular to *m* (α = 90°).

2. To construct a straight line *m* parallel to a given straight line *I* and at a distance *a* from it (Fig 1 right). Take a point *P* on *I* and erect the perpendicular to *I* at this point. Describe a circle with radius *a* about *P*. This intersects the perpendicular in two points *A* and *B*, such that *P* lies between *A* and *B*. Draw the lines parallel to *I* through *A* and *B*. There are two lines, *m*_{1} and *m*_{2} with the required property.