|
Question 476130: What is the difference between intersecting and perpendicular and parallel lines and can two lines exist that are not intersecting or parallel?
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! Two lines that intersect are simply two lines that at some point touch each other (cross each other). Take this character "X" for instance, the two lines that make the "X" character are intersecting lines.
Two perpendicular lines are two lines that intersect, but also the angle of intersection must be 90 degrees. For example, take the "+" character, the two lines that make the "+" character are perpendicular lines (intersecting at 90 degrees)
Two parallel lines are lines that never meet no matter how far we extend them. For example "||", the two lines in the "||" character(s) are parallel lines, they never touch each other, and if we extended them down into the ground of up into the sky they still would not intersect.
Now can there exist two lines that are neither intersecting nor parallel? Impossible, consider satisfying the first condition, if they never intersect then they never touch each other, and if they don't touch each other, then by definition they are parallel, which we don't want. Now let's try to satisfy the second condition, if they are parallel, then they never touch each other, which means they are not intersecting. So basically, if we have one, it fails the other, therefore it is impossible to have two lines that are neither intersecting nor parallel.
|
|
|
| |
