Question

Part A: Parallel lines are two lines that never meet. Find an example that contradicts this definition. How would you change the definition to make it more accurate?
Part B: Give an example of an undefined term and how it relates to parallel lines.​

Answer 1

Answer:

The problem in the first statement is that it does not say that the lines must be in the same plane.

Suppose in a 3D coordinate axis two lines as:

z = 0, y = 0 (this is the x-axis)

y = 1, x = 0 (this line is parallel to the z-axis but one unit above).

Those two lines are not parallel, and also never meet, so the definition is wrong.

The actual definition should be:

"Parallel lines are two lines that lie on the same plane and never meet"

B: The undefined terms are point, line, plane,...

An example can be "Plane", because if our lines do not lie on the same plane, then we can not use the concept of "parallel lines".