Question

select the postulate that proves this fact. if g and h are different points in plane r, then a third point exists in r not on \\(\overleftrightarrow{gh}\\). \\(\circ\\) postulate 1b: space contains at least four points not all on one plane. \\(\circ\\) postulate 2: through any two different points, exactly one line exists. \\(\circ\\) postulate 4: if two points lie in a plane, the line containing them lies in that plane. \\(\circ\\) postulate 5: if two planes intersect, then their intersection is a line. \\(\circ\\) postulate 1a: a plane contains at least three points not all on one line. \\(\circ\\) postulate 1: a line contains at least two points. \\(\circ\\) postulate 3: through any three points that are not one line, exactly one plane exists.

Explanation:

The problem states that if \( G \) and \( H \) (two different points) are in plane \( R \), then a third point exists in \( R \) not on \( \overleftrightarrow{GH} \). Postulate 1a says a plane has at least three non - collinear (not all on one line) points. Since \( G \) and \( H \) are on \( \overleftrightarrow{GH} \), the third point must not be on \( \overleftrightarrow{GH} \) to satisfy the non - collinear condition of the postulate, so this postulate proves the given fact.

Answer:

Postulate 1a: A plane contains at least three points not all on one line.