Is this conditional statement true? If 3 points form the vertices of a triangle, then they lie in the same plane.

It is true.

A plane requires
a minimum of 3 points. It is always a truth. Any 3 points detrmine a unique
plane.

Given a point  (say its cooerdinates say 2 dimension
or 3 dimensio or higher ), it is unique.

Given  two points
(the coordinates or location  of 2 points) , they determine a unique straight
line.

And like that given 3 points in silid geometry, they
detrmine a unique plane.

So the 3 vertices of a triangle
are always in a plane. Or Any 3 points in space are aways  form a plane or they are
coplanar.

Any four points need not be
coplanar.