📗 Introduction to Euclid's Geometry (Class 9)

Geometry

Study of shapes, figures, and their properties\

Euclid

Father of geometry\

Euclid's Elements

A collection of 13 books written by Euclid on geometry\

Axiom

A statement accepted without proof\

Postulate

Axiom specific to geometry\

Theorem

Statement that can be proved using axioms and postulates\

Euclid's 5 postulates

Basic rules about points, lines, and circles\

Postulate 1

A straight line may be drawn joining any two points\

Postulate 2

A terminated line can be produced indefinitely\

Postulate 3

A circle can be drawn with any centre and radius\

Postulate 4

All right angles are equal to one another\

Postulate 5

If two lines intersect a third such that sum of angles is less than 180°, they meet on that side\

Point

That which has no part\

Line

Breadthless length\

Surface

That which has length and breadth only\

Plane surface

A surface which lies evenly with straight lines on itself\

Undefined terms

Point, line, and plane are undefined but accepted\

Parallel postulate

Euclid's 5th postulate (basis of parallel lines)\

Equivalent version of postulate 5

Lines that never meet are parallel\

Geometrical construction

Based on postulates\

Euclidean geometry

Geometry based on Euclid's postulates\

Non-Euclidean geometry

Geometry that does not follow Euclid's postulate 5\

Use of axioms

To derive theorems logically\

Deductive reasoning

Reasoning from known facts or axioms