12 Granting that if two lines perpendicular to the same tran

12. Granting that if two lines perpendicular to the same transversal line meet on one side of that line, reflection about the midpoint of the interval between the two points where the lines meet the transversal shows that they must also meet on the other side. How do you know that these two points of intersection are not the same point? What other assumption must you introduce in order to establish that they are different?

Solution

Given that --------

Granting that if two lines perpendicular to the same transversal line meet on one side of that line, reflection about the midpoint of the interval between the two points where the lines meet the transversal shows that they must also meet on the other side.

a transversal is a line that passes through two lines in the same plane at two distinct points.

So, by this definition we can say that these two points are not same.