INTRODUCTION TO EUCLID'S GEOMETRY

The word geometry is derived from the Greek words "geo" meaning "earth" and "metron" meaning "measuring". Thus geometry means earth measurement.
Euclid was the first Greek mathematician who initiated a new way of thinking the study of geometry.

• Axioms: The basic facts which are taken for granted, without proof, are called axioms.
• Theorems: The conclusions obtained through logical reasoning based on previously proved results and some axioms constitute a statement which is known as a theorem or proposition.
• Point: A point is represented by a fine dot.
• Plane: The surface of a smooth wall or the surface of a sheet of paper or the surface of a smooth black board are close examples of a plane.
• Line: If we fold a piece of paper, the crease in the paper represents a geometrical straight line.
• Line segment: A line segment is a part of a line that is bounded by two distinct points, and contains every point on the line between its endpoints.

List of axioms:

• Axiom 1: A line contains infinitely many points.
• Axiom 2: Through a given point, there pass infinitely many lines.
• Axiom 3: Given two points A and B, there is one and only one line that contains both the points.

Collinear points: Three or more points are said to be collinear if there is a line which contains all of them.

Concurrent lines: Three or more lines are said to be concurrent if there is a point which lies on all of them.

Intersecting lines: Two lines are intersecting if they have a common point. The common point is called the "point of intersection".

Parallel lines: Two lines l and m in a plane are said to be parallel if they do not have a common point, i.e. they do not intersect. If l and m are parallel lines in a plane, we write l ॥ m.