GMAT Exam: A Simple Guide To Geometry - Lines

Descriptions of Lines
Lines in the same plane can be parallel or intersecting.

In geometry, plane is an undefined term. Intuitively, a plane is a two-dimensional, infinite surface.
Intersecting lines cross at a point in the plane.
Parallel lines never intersect. The distance between them is always the same. Perpendicular lines intersect at right angles.

Here are examples.


A tangent line to a circle intersects the circle in exactly one point.


Notation
The notation stands for the line containing the points A and B and extending infinitely in both directions.
To indicate is parallel to , write . To indicate is perpendicular to , write .
The line segment is a part of a line connecting the points A and B and includes A and B.
The points A and B are its endpoints. Its length is AB.

Congruent segments have equal lengths.

Useful Information About Lines in a Plane
- The shortest distance from a point to a line is the perpendicular distance from the point to the line.
- Two (distinct) lines that are perpendicular to the same line are parallel.
- A line that is perpendicular to one of two parallel lines is perpendicular to the other one too.
- A radius drawn to the point where a tangent line meets a circle is perpendicular to the tangent at that exact point.