Answer :
Answer:
Part 18) The railroad ties are parallel
Part 19) One railroad tie is perpendicular to both rails
Step-by-step explanation:
Part 18) The railroad ties are each perpendicular to one rail
we know that
if one line is perpendicular to several other lines, then the other lines are parallel
Conclusion:
If the railroad ties are each perpendicular to one rail then the railroad ties are parallel
That means----> The slopes of the railroad ties are equal and they are opposite reciprocal of the slope of the rail
Part 19) The rails are parallel. One railroad tie is perpendicular to one rail
we know that
if two lines are parallel and another line is perpendicular to one of them, then this line is perpendicular to both lines
Conclusion:
If One railroad tie is perpendicular to one rail, then one railroad tie is perpendicular to both rails
That means ---> The slopes of the railroad ties are opposite reciprocal to the slope of the rail
The railroad ties are each perpendicular to both rails, due to the geometric properties of parallel lines and perpendicularity, ensuring consistent distance and the safety of the train's journey.
The statements about the railroad tracks indicate certain geometric properties involving parallel lines and perpendicularity. From these statements, we can conclude that if the railroad ties are each perpendicular to one rail and the rails are parallel:
The railroad ties must also be perpendicular to the other rail because perpendicular lines intersect at a 90-degree angle. In a set of parallel rails, if a line (railroad tie) is perpendicular to one rail, it must be perpendicular to both due to the nature of parallel lines.
Since all the railroad ties are perpendicular to both rails, they serve as connectors between the two parallel rails, keeping a consistent distance between them.
This geometric relationship between the rails and the ties helps maintain the structure of the railroad, ensuring that the train can travel safely from one location to another.
