In geometry, a plane is defined as a flat, two-dimensional surface that extends infinitely in all directions. To properly identify or define a plane, we need to adhere to certain conditions as specified by geometric postulates.
### Postulate 1-2
This postulate states that a plane is determined by at least three non-collinear points. Let's break down what this means:
1. Points: A point represents an exact location in space and has no size, dimension, or volume.
2. Non-collinear points: Points that are not all located on the same straight line.
### Understanding with Examples:
1. Two Points:
- If you are given two points, you can only define a line, not a plane.
2. Three Collinear Points:
- If you are given three points that lie on the same straight line (collinear), they will still only define that line, not a plane.
3. Three Non-collinear Points:
- If you have three points that do not lie on the same straight line, those points will define a unique plane. This is because three non-collinear points can form a triangle, and any plane containing these three points must contain the entire triangle.
### Conclusion
Given the geometric postulate and understanding from the examples above, the least number of points needed to identify a plane is three, provided that these three points are not collinear.
So, the answer is:
- Three non-collinear points are the minimum number of points needed to uniquely identify a plane.
