MATHEMATICAL SYSTEM || UNDEFINED TERMS

• Mathematical system is divided into four parts: undefined terms, defined terms, postulates, and theorems.
• Undefined terms in geometry include terms that cannot be precisely defined.
• Defined terms in mathematics have a formal definition.
• Actions or postulates are statements which are accepted as true without proof.
• Theorems are statements that can be proven.
• The four parts of mathematical system: undefined terms, defined terms, actions postulates, and theorems, are related to one another.
• Under undefined terms, we have the point, the line, and the plane.
• For defined terms, we will be discussing collinear points, coplanar points, and the subsets of a line.
• Theorems under point line plane theorems include three theorems.
• The relationship of these four parts of mathematical system can be exemplified by using a set of objects.
• Coplanar points are points that lie in the same plane.
• A line extends infinitely in both directions and has three subsets: line segment, ray, and whole line.
• A whole line is the entire line.
• Non-coplanar points are points that do not lie in the same plane.
• A line segment is a part of a line consisting of two endpoints and all points between them.
• A plane is named by a single script capital letter.
• A plane is not a solid figure.
• A plane is a flat surface that extends infinitely along its length and width.
• Non-collinear points are points that do not lie on the same line.
• A ray is a part of a line consisting of an endpoint and all points on the line extending from it.
• Collinear points are points that lie on the same line.
• Two points on a line determine a unique line.
• A plane can also be named by any three points in the plane.
• A point can be represented by a sesame seed, the corner of a box, the tip of a finger, the tip of a marker, the tip of a needle, or any other small object.
• A line can be represented by an edge of a ruler, the edge of a notebook, the edge of a band paper, a headphone, or any other straight object.
• A plane can be represented by a sheet of paper, a piece of cardboard, a pencil, or any other flat object.