Summary

In this chapter, you have studied the following points:

1. Though Euclid defined a point, a line, and a plane, the definitions are not accepted by mathematicians. Therefore, these terms are now taken as undefineddefined.

2. Axioms or postulates are the assumptionsfacts which are obvious universal truths. They are not proved.

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

4. Some of Euclid’s axioms were :

(1) Things which are equal to the same thing are equalnot equal to one another.

(2) If equals are added to equals, the wholespart are equal.

(3) If equals are subtracted from equals, the differencessum are equal.

(4) Things which coincide differ with one another are equal to one another.

(5) The wholesome is greater than the part.

(6) Things which are double halves of the same things are equal to one another.

(7) Things which are halveswhole of the same things are equal to one another.

1. Euclid’s postulates were :

Postulate 1 : A straight regular line may be drawn from any one point to any other point.

Postulate 2 : A terminated indefinite line can be produced indefinitely.

Postulate 3 : A circle can be drawn with any centre and any radius diameter.

Postulate 4 : All right angles are equalnot equal to one another.