Determine whether the following is true or false: the vertices of a triangle determine a plane.
So let’s consider three points, the vertices of a triangle, which we’ll call 𝐴, 𝐵, and 𝐶. As these points form a triangle, this means that all three of them don’t lie on the same straight line. They are noncolinear.
One of the geometric postulates tells us that through any three noncolinear points, there is exactly one plane. The word exactly is key here. There is only one unique plane that contains all three points.
Therefore, the statement that the vertices of a triangle determine a plane is true.