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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 GH

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.

Respuesta :

aachen
Given that if G and H are different points in plane R, then a third point exists in R not on GH.

In other words, it means we have three non-linear points say G, H, I (not on the same line) where these three points make a triangle i.e. ΔGHI and this triangle is on plane R.

Only one postulate can prove this fact that is:-

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

Answer:

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

Step-by-step explanation:

Postualte 1a is the one we use to prove the fact showed, because based on this postulate a plane must have at least three points to exist. That means we cannot draw a plane with just two points, because the figure formed would be a line.

Remember, you always need three points to draw a plane, and only two point to draw a line.

Therefore, the right answer is the second choice, Postulate 1a.