CBSE 9th Maths

Introduction to Euclid Geometry

Euclid’s Definitions, Axioms or Postulates

• A point is that which has no part.
• A line is a breadthless length.
• The ends of a line are points.
• A straight line is a line which lies evenly with the points on itself.
• A surface is that which has length and breadth only.
• The edges of a surface are lines.
• A plane surface is a surface which lies evenly with the straight lines on itself.

Undefined Terms: There are some terms like point etc which have no definitions, these terms are called undefined terms.
In geometry, a point, a line and a plane (in Euclid’s words, a plane surface) are undefined terms.

Euclid’s Axioms

• Things which are equal to the same thing are equal to one another.
• If equals are added to equals, the wholes are equal.
• If equals are subtracted from equals, the remainders are equal.
• Things which coincide with one another are equal to one another.
• The whole is greater than the part.
• Things which are double of the same things are equal to one another.
• Things which are halves of the same things are equal to one another.