Chapter 3.3, Problem 13CE

To determine

To describe: the existence and uniqueness in given theorem.

Explanation of Solution

Given information:

Given theorem 3-8 states that:-

Through a point outside a line, there is exactly one line parallel to the given line.

Calculation:

Consider theorem 3-9 and reword it as two statements as follows:

Statement describing existence would be $-$ “There exists one line parallel to a line through a point outside that given line”.

Statement describing uniqueness would be $-$ “There is one only one line perpendicular to a line through a point outside that given line”.