Can Lines Be Infinite?

Do 2 intersecting lines determine a plane?

“If two lines intersect, then exactly one plane contains the lines.” …

“If two lines intersect, then they intersect in exactly one point.” and three noncollinear points define a plane..

Do any two planes intersect?

The intersection of two planes is a line. If the planes do not intersect, they are parallel. They cannot intersect at only one point because planes are infinite. … The intersection of planes happens in a three-dimensional space.

Do parallel lines exist?

Parallel Lines In Euclidean geometry a postulate exists stating that through a point, there exists only 1 parallel to a given line. … Therefore, Parallel lines do not exist since any great circle (line) through a point must intersect our original great circle.

Can a line intersect itself?

No line can intersect itself. You don’t have “a line”; you have four lines. You want to see if two of them intersect each other. You can either calculate the intersection explicitly or look at how the coordinates are labeled.

Do 2 points always create a line?

ANSWER: Never; Postulate 2.1 states through any two points, there is exactly one line. 26. If points M, N, and P lie in plane X, then they are collinear.

Why do parallel lines not meet?

By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. … Actually parallel lines cannot meet at a point or intersect because they are defined that way, if two lines will intersect then they will not remain parallel lines.

When two infinite planes intersect what do they form?

Answer and Explanation: When two planes intersect, they form a line.

Do skew lines intersect?

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. … Two lines that both lie in the same plane must either cross each other or be parallel, so skew lines can exist only in three or more dimensions. Two lines are skew if and only if they are not coplanar.

What contradicts parallel lines?

Take two parallel lines that are cut by a transversal. Since the lines are parallel, the consecutive interior angles of intersection are supplementary. Specifically, if the two parallel lines intersect, we have formed a triangle with angles that add up to more than 180 degrees, which is a contradiction.

Does 180 equal parallel lines?

The parallel case If the transversal cuts across parallel lines (the usual case) then the interior angles are supplementary (add to 180°). So in the figure above, as you move points A or B, the two interior angles shown always add to 180°. Try it and convince yourself this is true.

Can an infinite number of lines intersect a plane at one point?

1 Expert Answer If a line lies within the plane, then it intersects at an infinite number of points.

Are parallel lines coplanar?

Parallel lines are coplanar (they lie in the same plane) and never intersect. Below is an example of two parallel lines: Parallel lines never ______________________________ each other. … In a picture, we draw the symbol _____________ on both lines to show that the lines are parallel to each other.