Introduction to Euclid’s Geometry Class 9 Notes Maths - Chapter 5

Chapter: 5

What Are Introduction To Euclid’s Geometry ?

Undefined Terms

Euclid defined a point, a line, and a plane (i.e., a plane surface), but these definitions are not accepted by mathematicians. So, in geometry we take these terms as undefined terms.

Axioms, Postulates And Theorems

• Axioms or postulates are the assumptions which are obvious universal truth, i.e. they need not to be proved.

• The term postulates was used for the assumptions specific to geometry.

• The term axiom was used throughout mathematics and it is not specifically linked to geometry.

• Theorems are statements which are proved using definitions, axioms, previously proved statements and deductive reasoning.

Euclid’s Axioms

  • Axiom 1 : Things which are equal to the same thing are equal to one another.
  • Axiom 2 : If equals are added to equals, then the wholes are equal.
  • Axiom 3 : If equals are subtracted from equals, then the remainders are equal.
  • Axiom 4 : Things which coincide with one another are equal to one another.
  • Axiom 5 : The whole is greater than the part.
  • Axiom 6 : Things which are double of the some things are equal to one another.
  • Axiom 7 : Things which are halves of the same things are equal to one another.

Euclid’s Postulates

  • Postulate 1 : A straight line may be drawn from any one point to any other point.
  • Postulate 2 : A terminated line can produced indefinitely.
  • Postulate 3 : A circle can be drawn with any centre and any radius.
  • Postulate 4 : All right angles are equal to one another.
  • Postulate 5 : If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.