Concept explainers
To state: whether the given statement is true or false and also, to write the converse of the given statement.
Answer to Problem 23CUR
The given statement is false.
The converse is stated as follows:
If two lines are parallel, then they do not intersect.
Explanation of Solution
Given information: The given statement is ‘’If two lines do not intersect, then they are parallel’’
Consider the following diagram:
Here, the lines m and n are neither intersecting nor parallel.
m and n are basically skew lines.
(In three dimensional geometry, skew lines are two lines that neither intersect nor parallel)
Hence, if two lines do not intersect then they need not be parallel.
So, the given statement is false.
Converse of the statement is stated as follows:
If two lines are parallel, then they do not intersect.
Chapter 3 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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