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Concept explainers
a.
To describe: The given statement is true or false.
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 19CE
The statement is false.
Explanation of Solution
Given:
Statement a: Two lines perpendicular to a third line must be parallel.
Method used:
The lines are drawn according to given conditions.
According to given condition the lines are drawn as follows:
If two lines in space are perpendicular to a third line, they are not parallel always as shown in Figure-1 and Figure-2.
Hence, the statement is false.
Conclusion:
The statement is false.
b.
To describe: The given statement is true or false.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 19CE
The statement is true.
Explanation of Solution
Given:
Statement b. In a plane two lines perpendicular to a third line must be parallel.
Method used:
The lines are drawn according to given conditions.
According to given condition the lines are drawn as follows:
In a plane, if two lines are perpendicular to a third line, they are always parallel as shown in Figure-2.
Hence, the statement is true
Conclusion:
The statement is true
c.
To describe: The given statement is true or false.
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 19CE
The statement is true.
Explanation of Solution
Given:
Statement c: In a plane two lines parallel to a third line must be parallel.
Method used:
The lines are drawn according to given conditions.
According to given condition the lines are drawn as follows:
If in a plane two lines are parallel to a third line, they are parallel to each other as shown in Figure-3.
Hence, the statement is true.
Conclusion:
The statement is true.
d.
To describe: The given statement is true or false.
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 19CE
The statement is true.
Explanation of Solution
Given:
Statement a: Any two lines parallel to a third line must be parallel.
Method used:
The lines are drawn according to given conditions.
According to given condition the lines are drawn as follows:
Any two lines are parallel to a third line, are always parallel to each other as shown in Figure-3 in part (c).
Hence, the statement is true.
Conclusion:
The statement is true.
Chapter 3 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
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