Lines - GMAT Math Study Guide

Definitions

  • Line - A series of connected points that extends out infinitely.
  • Line Segment - A portion of a line.
  • Parallel Lines - Two or more lines that never intersect.
  • Perpendicular Lines - Two lines whose intersection forms a 90° angle.

Line Basics

In the world of geometry, a line refers to a straight line that extends out infinitely in both directions. For any two points, there is one and only one line that connects them. A line segment is a portion of a line from one point to another. For example:

Line l can be called the line nm, sometimes denoted nm. The portion of the line from n to m is a line segment. nm can also denote the line segment as well as the length of the line segment. Context is the best means to determine the use of the notation.

Parallel Lines

Two lines in the same plane are said to be parallel if they never cross or intersect. In coordinate geometry, parallel lines have the same slope but different x-intercepts. For example:

parallel lines

Lines D and E are parallel (denoted D || E), while lines F and G are not parallel since they intersect. Since the slope of parallel lines must be the same, the slope of lines D and E is the same. Note that parallel lines do not have to be horizontal.

Perpendicular Lines

Two lines are perpendicular when they intersect and form 90° angles. For example:

Lines K and H are perpendicular while lines P and Q are not perpendicular. A right angle symbol indicates that K and H are perpendicular (the symbol is composed of the two lines that form a square at the intersection of lines K and H).