Class 9 Maths Euclid Geometry Definition, Axioms, Postulates & Theorems

Definition, Axioms, Postulates & Theorems

Greek mathematicians of Euclid’s time thought of geometry as Abstract model of world they lived in. The notions of point, line, plane (or surface) and so on were derived from what was seen around them. From studies of the space and solids in the space around them, an abstract geometrical notion of a solid object was developed.

A solid has shape, size, position, and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from another, and are said to have no thickness. The boundaries of the surfaces are curves or straight lines. These lines end in points.

Consider the three steps from solids to points (solids-surfaces-lines-points). In each step we lose one extension, also called a dimension. So, a solid has three dimensions, a surface has two, a line has one and a point has none.

Solid (3D) à Surfaces (2D)  à Lines (1D) à Points (0D).

Starting with definition, Euclid assumed certain properties which are not to be proved. These assumptions are called obvious Universal Truth; He divided these truths in 2 parts

1. Axioms: Common to all domains. E.g.: Whole is greater than Part
2. Postulates: Specific to Geometry. E.g.: A circle can be drawn using a center & a radius.

Theorems are statements which are proved using the definition, axioms, postulates, previously proved theorems & deductive reasoning.  E.g.: Diameter divides circle in 2 part is a theorem that has proof.

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