Concept explainers
To find: The proof of the given theorem.
Explanation of Solution
Given information:
The given theorem is, “In a plane, if two lines are perpendicular 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 the two lines is perpendicular to a same line, then the slope of both lines will be same and hence in a plane, if two lines are perpendicular 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
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