Point Existence Postulate for Planes
The Point Existence Postulate for Planes states that if three non-collinear points are given, then there exists exactly one plane that contains all three points
The Point Existence Postulate for Planes states that if three non-collinear points are given, then there exists exactly one plane that contains all three points.
To understand this postulate, let’s break it down:
1. “Points”: Points are basic building blocks in geometry that have no dimension. They are usually represented by dots and are used to define shapes, lines, and planes.
2. “Collinear points”: Collinear points are points that lie on the same straight line. In this postulate, it is explicitly stated that the three points must not be collinear.
3. “Non-collinear points”: Non-collinear points are points that do not lie on the same straight line. In other words, they are not collinear.
4. “Plane”: A plane is a flat surface extending infinitely in all directions. It has two dimensions – length and width – and is represented by a parallelogram or a quadrilateral in geometry.
Now, based on the Point Existence Postulate for Planes, if we have three points that are not collinear, there will always be exactly one plane that contains all three points. This means that these three points will uniquely define a plane, and no other plane will contain these three specific points.
For example, if we have points A, B, and C that are non-collinear, we can say that there will be a unique plane that passes through these three points. If we were to choose any other three non-collinear points, they would also define a unique plane.
This postulate is a fundamental concept in geometry and is used to establish the existence of planes based on given points. It helps us understand the relationship between points and planes and is essential when solving problems or proving theorems in geometry.
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