# Lines - GMAT Math Study Guide

## Table of Contents

## 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:

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*).