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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.
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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.
Does an isosceles triangle have two equal lines?
Yes. Always
Does a triangle always have diagonal lines?
The sides of the triangle will always meet at angles such that two of them will appear 'diagonal'. But these are not defined as diagonal lines. There are actually no diagonals intersecting any triangle. Try drawing one and connecting the vertices - it doesn't work and you simply end up tracing over the lines that define the triangle.
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.
Will the perpendicular bisectors of a right triangle always intersect?
yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)
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.
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 type of triangle always has 3 lines of symmetry?
An equilateral triangle.
What has the shape of a triangle?
A triangle is 3 lines or sides connected together at their ends. These lines are not always the same lengths.
Does an isosceles triangle have two equal lines?
Yes. Always
Does a triangle always have diagonal lines?
The sides of the triangle will always meet at angles such that two of them will appear 'diagonal'. But these are not defined as diagonal lines. There are actually no diagonals intersecting any triangle. Try drawing one and connecting the vertices - it doesn't work and you simply end up tracing over the lines that define the triangle.
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.
Are there oblique lines in a triangle?
Yes, there can be oblique lines in a triangle. However, there can only be oblique lines in a triangle if the triangle is considered to be a 'right' triangle.
What is a counterexample of All rectangles have two lines of symmetry?
Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.
What kind of of triangle has 3 lines of symmetry?
An EQUILATERAL Triangle. Two lines of symmetry is ISOSCELES Triangle No lines of symmetyry is SCALENE Triangle.
Does a acute triangle have parallel lines?
There are no parallel lines in a triangle.
Will the perpendicular bisectors of a right triangle always intersect?
yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)
