Choose the phrase that completes the following statement as stated by the point, line, and plane postulates:
Once plane___________ passes through three noncollinear points.
a. never
b. sometimes
c. always
d. point, line, and plane postulates do not address this topic directly.
To find the answer to this question, we need to understand the definitions of the terms "point," "line," and "plane" as well as the postulates related to them.
According to the point postulate, a point is a basic geometric figure with no dimensions.
According to the line postulate, a line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points.
According to the plane postulate, a plane is a flat surface that extends infinitely in all directions. A plane is made up of an infinite number of lines.
Based on these definitions, we can conclude that a plane always passes through three noncollinear points. This is because any three noncollinear points will define a unique plane. Therefore, the correct answer to the statement is option c. always.
The postulates specifically state that a plane is determined by three noncollinear points, making it a fundamental property of planes. Therefore, option d, which states that the point, line, and plane postulates do not address this topic directly, is incorrect.
So, the correct answer to the statement is c. always.