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If two lines intersect, they intersect in exactly one point. This point is the location where the two lines cross each other in a two-dimensional plane. In Euclidean geometry, two distinct lines can either intersect at one point or be parallel, in which case they do not intersect at all.
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If two lines intersect then they lie in one plane. Is this true always sometimes or never?
always. if two lines intersect, then exactly one plane contains the lines.
When two or more lines intersect at a point they are said to be?
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
Can two skew lines intersect in exactly one point?
always
Does perpendicular lines intersect in exactly two points?
No, just one point.
If two lines intersect they intersect in an infinite number of points true or false?
False. If two lines intersect, they do so at exactly one point, provided they are not parallel. In Euclidean geometry, two distinct lines can either intersect at a single point or be parallel and never intersect at all.
Can two lines intersect in exactly one line?
always
If two lines intersect then they lie in one plane. Is this true always sometimes or never?
always. if two lines intersect, then exactly one plane contains the lines.
When two or more lines intersect at a point they are said to be?
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
Can two skew lines intersect in exactly one point?
always
Does perpendicular lines intersect in exactly two points?
No, just one point.
If two lines intersect they intersect in an infinite number of points true or false?
False. If two lines intersect, they do so at exactly one point, provided they are not parallel. In Euclidean geometry, two distinct lines can either intersect at a single point or be parallel and never intersect at all.
How many Counterexamples are needed to disprove the conjecture two lines in a plane always intersect at exactly one point?
To disprove the conjecture that two lines in a plane always intersect at exactly one point, only one counterexample is needed. A single example of two lines that do not intersect, such as two parallel lines, is sufficient to show that the conjecture is false. Therefore, one counterexample is enough to invalidate the claim.
Which statement is trueJax drew a line through point A and point B. Chris also drew a line through the two points.?
The two lines are identical.
Two lines only intersect at exactly one point?
Two straight lines, whether they're in the same or different planes, must intersect at either one point or else at no points.
Is any two lines lie in exactly one plane?
Two lines can lie in one plane. For example, parallel lines are lines that intersect and lie in the same plane.
How many times does perpendicular lines intersect?
Perpendicular lines intersect at exactly one point. This point is where the two lines cross each other, forming a right angle (90 degrees) between them. If two lines are perpendicular, they will not intersect at any other point.
Do two distinct planes intersect in a pair of lines?
No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.
