Which pair of undefined terms is used to define the term parallel lines?
A. point and line
B. plane and line
C. point and ray
D. ray and line
Answer: A. point and line
In the given case of ‘parallel lines’, the couple of unspecified terms to describe is point and line. It is significant to note that in any branch of geometry, there are basic assumptions that are commonly referred to as undefined notions since they cannot be defined in terms of other definitions that are simpler. Point and line are two of the undefined concepts that form the basis of the geometric understanding of parallel lines and other geometry concepts.
Intercepting two lines are two straight lines in the same plane that never meet however long they are drawn. This definition is based on two fundamental elements, points and lines. A line is defined as a set of points that goes to infinity on both ends whereas a point on the other extreme is a geometric entity with no dimension. Using these undefined terms, we can construct the definition of parallel lines: two lines are parallel if they both lie in the same plane and they do not intersect at any point.
For example, let there be two lines drawn on a sheet of paper; these two lines do not have a common point as they may be produced to infinity. These lines are parallel. Railroad tracks are another form of parallel lines that exist in the real world. The rails never converge and the distance between them is equal at every point of the wheel’s revolution. In the coordinate geometry the given lines y = 2x + 1 and y = 2x + 3 are parallel since both lines have the same slope that is 2 but different y-intercepts, so they do not intersect each other.
Thus, the undefined terms of point and line are the basis through which mathematicians can construct other geometrical concepts and proofs. With the help of this approach, it is possible to provide for reasonable and systematic construction of geometric principles based on these four crude and unadmitted notions.
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