parallel lines?

Question

What are the elementary properties of parallel lines?

Answer 1

Their elementary properties are that they don't intersect, ever.

Answer 2

No, they don't. They stay the same distance apart forever. Draw a horizontal line. Then draw two lines doing up-and-down. The last two lines are parallel. They are both perpendicular to the horizontal line. If the two vertical lines were to intersect, then you would have a triangle. Now, at what angle would the two lines intersect? Obviously, if two lines intersect, the angle of intersection must be positive, since, if the angle were zero degrees, they would be the same line. Now the sum of the angles inside any triangle is 180 degrees. The two parallel lines are each perpendicular to the horizontal line, so those angles are right angles. The sum of those two angles is already 180 degrees, so that doesn't leave a positive angle of intersection for the parallel lines. So they cannot intersect. I hope this helps! Edit: As some of the other posters have pointed out, this is only the case in Euclidean geometry. In other geometries, it depends upon the definition of parallel given.

Answer 3

Parallel lines are lines that lie in the same plane but do not have a point of intersection (i.e a point where they meet). The corresponding angles, alternate angles are congruent (of same measure). Parallel lines are LINES: they have no specific beginning and no end.
If line 'a' is parallel to line 'b' and line 'b' is parallel to line 'c' then line 'a' is parallel to line 'c'.
The line cutting across to or more parallel lines is called the transversal. There can be more than just one tranversal. If three parallel lines make congruent intercepts on any transversal then they make congruent intercepts on any other transversal. (For proof of this statement and details regarding alternate and corresponding angles, please email me at: [e-mail].)
The vertical distance between two parallel lines remains constant throughout. Hence, if two or more triangles are inscribed in two parallel lines the they will have same height.
And one more thing, parallel lines are denoted by the symbol 'll'. For eg. if we want to say line 'l' is parallel to line 'm' we write it as:
line 'l' ll line 'm'. Lines are always denoted using small alphabets, unlike the names of angles and triangles.

Answer 4

parallel lines are of course parallel to each other. if two lines are parallel to each other a perpendicular drawn on any of the lines at any point on the line will always be perpendicular to the other line too. if a line is drawn intersecting the two parallel lines, the vertically opposite angles created by the intersecting line are always equal.

Answer 5

well if 2 lines are parrles then the will never meet

SORRY IMAGE CANNOT COME

Here, angle PBD= angle SDB and similarly the other two angles in a property called that interior alterante angles are equal.

Similarly, exterior alt. angles will also be equal.

The angles on same side AE will be supplementary (180)

The corresponding angles will also be equal

Answer 6

they have to have the same slope as another line, and can have either the same y-intercept as that line or a different y-intercept line, the only difference is that the same y-intercept gives you an infinite solution and the one with a different y-intercept gives you no solution.

For ex:

y = ax + b and y = ax + b gives you infinite solutions, and they are parallel

y = ax + b and y = ax - b gives you no solution and they are parallel.

Answer 7

1)They never intersect
2)They can be curved (Never mind as long as they're parallel)
3)The perpendicular to one is perpendicular to the other..

Answer 8

a) straight lines;
b) equal distance apart;
c) stretch to infinity.

Answer 9

Must always be same distance apart

Answer 10

stretch to infinity.
have the same slope.
dont intersect.