Question

a table with four legs will sometimes wobble if one leg is shorter than the other three, but a table with three legs will not wobble. select the postulate that substantiates this fact.
postulate 3: through any three points that are not one line, exactly one plane exists.
postulate 2: through any two different points, exactly one line exists.
postulate 1: a line contains at least two points.
postulate 5: if two planes intersect, then their intersection is a line.
postulate 4: if two points lie in a plane, the line containing them lies in that plane.
postulate 1b: space contains at least four points not all on one plane.
postulate 1a: a plane contains at least three points not all on one line.

Explanation:

A three - legged table has its three legs' endpoints as three non - collinear points. By Postulate 3, these three points define exactly one plane, so the table is stable. For a four - legged table, the four endpoints may not all lie on this single plane (since four points can be non - coplanar or not all satisfy the three - non - collinear - point - plane condition), so when one leg is shorter, the table wobbles as the four points don't lie on a single stable plane.

Answer:

Postulate 3: Through any three points that are not one line, exactly one plane exists.