Question

construct arguments determine whether the statement is always, sometimes, or never true. justify your argument. points x and y are in plane z. any point collinear with points x and y is in plane z. select choice v postulate select choice v states that if two points select choice v in a plane, then the entire line containing those points select choice v in that plane.

Explanation:

Step1: Recall Plane Postulate

The postulate about planes and lines: If two points lie in a plane, then the entire line containing those points lies in that plane.

Step2: Apply to the Problem

Points \( X \) and \( Y \) are in plane \( Z \). A point collinear with \( X \) and \( Y \) is on the line \( XY \). By the postulate, since \( X \) and \( Y \) are in plane \( Z \), the line \( XY \) (and thus any point on it) is in plane \( Z \). So the statement is always true. The postulate used is: "If two points lie in a plane, then the entire line containing those points lies in that plane."

Answer:

The statement is always true. The postulate (If two points lie in a plane, then the entire line containing those points lies in that plane) justifies it: since \( X,Y \) are in plane \( Z \), the line \( XY \) (and any collinear point with \( X,Y \)) is in plane \( Z \).