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What is a counterexample to this conjecture if three lines lie in the same plane then they intersect in at least one point?
A counterexample to the conjecture is when three parallel lines lie in the same plane. In this case, none of the lines intersect at any point, demonstrating that it is possible for three lines in the same plane to not intersect at all. Therefore, the conjecture is proven false.
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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.
What is a counterexample for three coplainar lines always make a triangle?
A counterexample to the statement that three coplanar lines always form a triangle is when all three lines are parallel. In this case, the lines do not intersect at any point, and therefore, they cannot form a triangle. Another example is when two lines are coincident (overlapping) and the third line intersects one of them but does not intersect the other, failing to create a triangle.
What is the term for lines that don't intersect?
Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.
Do parallel intersect?
no they are straight lines that never intersect, intersecting lines intersect.
Do skew lines always intersect?
Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.
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.
What is a counterexample for three coplainar lines always make a triangle?
A counterexample to the statement that three coplanar lines always form a triangle is when all three lines are parallel. In this case, the lines do not intersect at any point, and therefore, they cannot form a triangle. Another example is when two lines are coincident (overlapping) and the third line intersects one of them but does not intersect the other, failing to create a triangle.
Do perpendicular lines intersect in at least two points?
Perpendicular lines intersect at one point only.
What is a counterexample for three coplanar lines always make a triangle?
If at least two of the three lines are parallel, the three lines will not form a triangle.
Counterexample for two lines in a plane always intersect in exactly one point?
Line #1 ==> Y = x Line #2 ==> Y = x + 1 These two lines are parallel, have no points in common, and never intersect. (3 ways to say the same thing)
Do perpendicular lines intersect in and at least to points?
Perpendicular lines are lines that always intersect either at just one point, two points or several more.
What is parallel planes?
Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect
What is the term for lines that don't intersect?
Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.
Do parallel intersect?
no they are straight lines that never intersect, intersecting lines intersect.
Do skew lines always intersect?
Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.
Which phrase describes perpendicular lines the lines never touch or the lines intersect at a right angle or the lines intersect at an acute angle or the lines intersect at a obtuse angle?
Lines that intersect at right angles.
Do lines that skew intersect?
No. Skew lines do not intersect
