​Perpendicular and Parallel Postulates

About Geometry Worksheet Assignment 2.19:     

 

Assignment 2.19 is an introduction to two postulates about parallel and perpendicular lines and the definition of distance between a point and a line and between parallel lines.

 

Prerequisite Skills: Identify and name perpendicular lines (Assignment 2.16).  Measure line segments (Assignment 1.11).  Identify and name parallel lines (Assignment 1.6).

 

Postulates:  In a plane, there is one and only one line that is perpendicular to a given line through a given point.

 

                          In a plane, lines perpendicular to the same line at distinct points are parallel.
 

                          Through a point not on a lie, there is exactly one line that is parallel to the line.

 

Definitions:  The distance from a point to a line is the length of a line segment that is perpendicular to the line with endpoints at the point and on the line. 

                                

                          The distance between two parallel lines is the length of a line segment that is perpendicular to the lines with an endpoint on each line.