determine whether each conjecture is true or false. Give a counterexample for any false conjecture
Given: Points A and B are collinear.
Conjecture: Points A and B form a line.
Unless they are at the same point, any two points form a line and are therefor collinear. So the conjecture is true, but not very interesting.
The conjecture that points A and B form a line is true. If points A and B are collinear, that means they lie on the same straight line. Therefore, the conjecture is true.
To determine whether the conjecture is true or false, we need to understand the definitions of the terms involved.
The given statement states that points A and B are collinear. In geometry, collinear points are points that lie on the same straight line. So, according to the given information, points A and B lie on the same line.
The conjecture states that points A and B form a line. In geometry, a line is defined as a straight path that extends infinitely in both directions.
To verify the truth of the conjecture, we can compare the definitions. Since the given information already says that points A and B are collinear, which means they lie on the same line, the conjecture is true.
No counterexample is necessary in this case, as the conjecture is true based on the given information.