To find: The proof of the given theorem.
Explanation of Solution
Given information:
The given theorem is, “If two lines are parallel to the same line, then they are parallel to each other”.
The parallel lines are the group of lines which never intersect each other or can say meet at infinity. The distance between the two parallel line is same at each point and the distance between two parallel lines is the length of any perpendicular segment joining the two lines. The slopes of the parallel lines are same, but they do not have same y -intersect.
If two lines are parallel then their slopes are same, so if wo lines are parallel to the same line, then the slopes of all lines will be same and hence if two lines are parallel to the same line, then they are parallel to each other.
Thus, the given theorem is proved.
Chapter 10 Solutions
BIG IDEAS MATH Integrated Math 1: Student Edition 2016
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education