Final answer:
A plane is defined to contain at least two lines because any two points can form a line, and a triangle on a plane, having three vertices, validates the possibility of at least three lines, where at least two lines lie completely within the plane.
Step-by-step explanation:
The conjecture that a plane contains at least two lines can be understood better by considering the principles of geometry. When we think of a triangle, we are considering a three-sided figure that lies on a plane with its three angles adding up to 180 degrees. This is because any two points on a plane can be connected to form a line, and since a triangle has three vertices, there are at least three possible lines that can be drawn from these points. Out of these, at least two must lie completely in the plane, thus proving the initial conjecture that a plane must contain at least two lines.
In geometry, and particularly in the algebra of vectors in two dimensions, the principles that enable the drawing of these conclusions are well established. When vectors are in a plane, they follow the commutative property of vector addition, where A + B = B + A. This simplifies the process of constructing resultant vectors, using both geometric constructions and trigonometry, which is a common practice in navigation.
Furthermore, considering vector addition or the definition of a plane in higher dimensions does not change the fact that at least two non-collinear vectors (or points) in a plane will determine a unique plane. Therefore, it's clear that a plane will indeed have at least two lines.