To identify the postulate that describes the relationship between points [tex]\(P\)[/tex], [tex]\(Q\)[/tex], and [tex]\(M\)[/tex] when [tex]\(M\)[/tex] is between [tex]\(P\)[/tex] and [tex]\(Q\)[/tex], and given that all three points are collinear, we consider the statement provided:
"If Point [tex]\(M\)[/tex] is between points [tex]\(P\)[/tex] and [tex]\(Q\)[/tex], and [tex]\(P, Q\)[/tex], and [tex]\(M\)[/tex] are collinear, then [tex]\(PM + MQ = PQ\)[/tex]."
Let's examine the given options:
a) Midpoint: This refers to the point that divides a segment into two equal parts. This is not directly related to the given statement, as the midpoint has more specific implications about equality of segments.
b) Ruler Postulate: This postulate states that the distance between any two points is the absolute value of the difference of the coordinates of these points. While this postulate deals with measurements and distances, it is not specifically about the relationship described in the given statement.
c) Segment Bisector: This term is used for a line, segment, or ray that divides a segment into two equal parts. Similar to the midpoint, it is not directly applicable to the given scenario.
d) Segment Addition Postulate: This states that if a point is between two other points on a line segment, then the sum of the lengths of the smaller segments is equal to the length of the entire segment. This perfectly matches the given statement: [tex]\(PM + MQ = PQ\)[/tex].
Therefore, the correct postulate that matches the given statement is the Segment Addition Postulate.
So the correct answer is:
d) Segment Addition Postulate.
