# Line

A line is a collection of points along a straight path extending indefinitely in both directions. This is indicated by the arrows at each end, shown in the figure below.

A line has one dimension, its length. Two non-overlapping points determine a unique line and we can name the line with those two points or any other two points on the line.

Lines are used in shapes, angles, and many other geometric contexts.

## Lines and angles

When two non-overlapping lines intersect at a point, two pairs of vertical angles are formed.

When 2 non-overlapping lines never intersect, they are called parallel lines.

When 2 lines intersect at a right angle, we say the lines are perpendicular to each other.

## Lines and planes

### Lines and polygons

Three or more intersecting lines can form a polygon whose vertices are the points at which the lines intersect.

Line l, m, n above intersect at points P, Q, and R forming triangle PQR. Also, P, Q, R are the vertices for the triangle formed.

### Determination of planes

A plane can be determined in a number of ways:

• Three points that are not on a single line can determine a plane
• A line and a point that is not on the line can determine a plane
• Two non-overlapping parallel lines determine a plane
• Two intersecting lines determine a plane

### Properties of planes

• Relative to a plane, a line can only be parallel to the plane, intersect it at a single point, or be contained in the plane (intersect it at all points)
• A line divides a plane into two equal parts (since a plane extends indefinitely too).
• Two planes can only either be parallel, or intersect along a line
• If two planes intersect, their intersection is a line.
• If two lines are perpendicular to the same plane, the two lines must be parallel (as long as they are not the same line)
• If two planes are perpendicular to the same line, the two planes must be parallel (as long as they are not the same plane)