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.
Yes. Always
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.
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.
yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)
If at least two of the three lines are parallel, the three lines will not form a triangle.
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.
An equilateral triangle.
A triangle is 3 lines or sides connected together at their ends. These lines are not always the same lengths.
Yes. Always
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.
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.
Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.
An EQUILATERAL Triangle. Two lines of symmetry is ISOSCELES Triangle No lines of symmetyry is SCALENE Triangle.
There are no parallel lines in a triangle.
yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)
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)