Introduction toEuclid’s Geometry
A theorem is a statement that requires a proof. Whereas, a basic fact which is taken for granted, without proof, is called an axiom.
Example of Theorem: Pythagoras Theorem
Example of axiom: A unique line can be drawn through any two points.
- Line segment: The straight path between two points is called a line segment.
- Ray: A line segment when extended indefinitely in one direction is called a ray.
- Intersecting Lines: Two lines meeting at a common point are called intersecting lines, i.e., they have a common point.
- Parallel Lines: Two lines in a plane are said to be parallel, if they have no common point, i.e., they do not meet at all.
- Half-line: A ray without its initial point is called a half-line.
- Concurrent lines: Three or more lines are said to be concurrent, if they intersect at the same point.
- Collinear points: Three or more than three points are said to be collinear, if they lie on the same line.
- Plane: A plane is a surface such that every point of the line joining any two points on it, lies on it.
- Six points: A,B,C,D,E,F
- Five line segments: , , , ,
- Four rays: , , ,
- Four lines: , , ,
- Four collinear points: M,E,G,B
- and their corresponding point of intersection is R. and their corresponding point of intersection is P.
- , , and their point of intersection is R.
- Three rays are: , ,
- Two line segments are: ,
- An infinite number of lines can be drawn to pass through a given point.
- One and only one line can pass through two given points.
- Two given lines can at the most intersect at one and only one point.
- , ,