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 1: A line contains at least two points. Postulate 1a: A plane contains at least three points not all on one line. Postulate 1b: Space contains at least four points not all on one plane. Postulate 2: Through any two different points, exactly one line exists. Postulate 3: Through any three points that are not one line, exactly one plane exists. Postulate 4: If two points lie in a plane, the line containing them lies in that plane. Postulate 5: If two planes intersect, then their intersection is a line.

Answer 1

postulate 3 would be the answer

Answer 2

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

Explanation:

The postulate 3 substantiates the presented fact, because a table with three legs will not wobble based on that postulate.

This postulate states that three points non-collinear, they form one plane, and this plane is unique, that's why the table won't wobble, all legs are in the same plane, and that plane is the floor. If those legs weren't in the same plane (the floor), they would wobble, because some leg would upper than the other ones.

Therefore, the right answer is Postulate 3.