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How do you negate the euclidean parallel postulate?
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
What is the name of an intersection of two nonparallel lines in a plane?
a point
What is Defined by distinct lines which intersect at right angles and at exactly one point.?
They are said to be perpendicular lines.
Can two distinct lines intersect in more than one point?
FALSE!!
What does intersecting lines mean?
Intersecting lines are those that lie in the same plane and cross each other at some point. Unless they are parallel, lines in the same plane always cross.
Given plane A and point C which is not on plane A How many lines can be drawn through point C that are perpendicular to plane A?
400
Point A lies outside of plane P how many lines can be drawn parallel to plane P that pass through point A?
Only one line can be drawn parallel to plane P that passes through point A. This line will be oriented in the same direction as the plane, remaining equidistant from it. All other lines passing through point A will either intersect the plane or be skew to it.
Through a given point how many lines can be drawn perpendicular to a given plane?
Through a given point, an infinite number of lines can be drawn perpendicular to a given plane. Since any line that extends from the point to the plane at a right angle can be considered perpendicular, and this can occur at various angles around the point, there are no restrictions on the direction of these lines as long as they maintain the perpendicular relationship. Hence, the answer is infinite lines.
How many lines can be drawn through one point?
uncountable lines can be drawn through one point.
How many lines can be drawn perpendicular to a given plane?
Through a given plane, an infinite number of lines can be drawn perpendicular to it. For any point on the plane, there exists exactly one line that is perpendicular to the plane at that point. However, since there are infinitely many points on the plane, this leads to an infinite number of perpendicular lines overall.
Can the lines of a plane intersect?
All non-parallel lines in a plane will intersect at some point in the plane.
Lines on a hyperbolic plane are considered to be?
Hyperbolic geometry is a beautiful example of non-Euclidean geometry. One feature of Euclidean geometry is the parallel postulate. This says that give a line and a point not on that line, there is exactly one line going through the point which is parallel to the line. (That is to say, that does NOT intersect the line) This does not hold in the hyperbolic plane where we can have many lines through a point parallel to a line. But then we must wonder, what do lines look like in the hyperbolic plane? Lines in the hyperbolic plane will either appear as lines perpendicular to the edge of the half-plane or as circles whose centers lie on the edge of the half-plane
Can two distinct lines intersect in more than one point explain?
Yes. Any two distinct lines of longitude, for example, meet at two points - the poles. On a plane, though, two points define a unique line. So if two lines intersect at more than one point they must be coincident.
What term applies to two lines in the same plane if they have no common plane?
If they are in the same plane, then they share a common plane. Did you mean to say common point. If that's the case where they are in the same plane, but do not share a common point, then they are parallel lines.
Do skew lines intersect if they are in the same plane?
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
What parallel lines intersect?
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
Describe a point a line and plane?
points that lines in the same plane are coplanor
