
Concept explainers
(a)
To state: whether the given statement is true or false.
(a)

Answer to Problem 2MRE
The given statement is true
Explanation of Solution
Given information:
The given statement is ‘’If two lines are parallel, then they are not skew.’’
Lines that are neither intersecting nor parallel are skew lines.
The given statement is ‘’If two lines are parallel, then they are not skew.’’
As per the definition of skew lines, as the lines are parallel, they are not skew.
(b)
To state: the converse of the given statement
(b)

Answer to Problem 2MRE
The converse is “If two lines are not skew, then they are parallel”
Explanation of Solution
First write the definition of skew lines and parallel lines.
Lines that are neither intersecting nor parallel are skew lines.
Lines that keep a fixed minimum distance and do not intersect are said to be parallel.
The given statement is ‘’If two lines are parallel, then they are not skew.’’
Now write the converse of the given statement.
The converse is “If two lines are not skew, then they are parallel”
(c)
To state: whether the converse of the given statement is true or false.
(c)

Answer to Problem 2MRE
The converse is false.
Explanation of Solution
First write the definition of skew lines and parallel lines.
Lines that are neither intersecting nor parallel are skew lines.
Lines that keep a fixed minimum distance and do not intersect are said to be parallel.
As per part (b), the converse of the given statement is stated as follows:
The converse is “If two lines are not skew, then they are parallel”
Now if two lines are not skew then they can be either intersecting or parallel.
But it’s not necessary then if two lines are not skew, then they are parallel only. They can be intersecting also.
So, the converse statement is false.
Chapter 3 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
Additional Math Textbook Solutions
Thinking Mathematically (6th Edition)
Elementary Statistics
Elementary Statistics: Picturing the World (7th Edition)
Elementary Statistics (13th Edition)
Algebra and Trigonometry (6th Edition)
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