Final answer:
A counterexample to the statement "If three distinct points lie in a plane, then the points can form a triangle" could be three collinear points, which cannot form a triangle despite lying in the same plane.
Step-by-step explanation:
Seeking a counterexample for the conditional statement "If three distinct points lie in a plane, then the points can form a triangle," requires us to find a scenario where three distinct points lie in a plane but do not form a triangle. A counterexample can be three collinear points, meaning they lie on the same straight line. In this case, despite fulfilling the condition that they lie in a plane, these points cannot form a triangle because a triangle requires three non-collinear points that connect to create three straight sides.
To further understand counterexamples, we can refer to other conditionals such as "If it has rained, the ground will be wet." A counterexample in this instance could be if rain fell while a canopy covered the ground, hence the ground being dry despite the rain.
In conclusion, a counterexample disproves a conditional statement by satisfying its premise while failing to meet its conclusion. This reinforces the idea that in a conditional statement, the premise only suggests a possible outcome but does not guarantee it.