Question

Write any two axioms given by Euclid.

Answer 1

Hint: An axiom or a postulate is a statement that is self-evidently true or assumed to be true. They serve as starting points to further prove more complex statements and expressions. Euclid gave 5 axioms which formed the basis of Euclidean Geometry.

Complete step-by-step answer:
The two axioms given by Euclid are-
1. Things which are equal to the same thing are also equal to one another. This can be shown with an example-
Let a = b and a = c, here c and b are two things equal to the same thing, a. So b and c should also be equal, that is, b = c.

2. If equals are added to equals, the holes are equal. This can be shown with an example-
Let a = c and b = d
Let a + b = x
Now if we find the value of c + d-
=c + d
=a + b (a=c and b=d)
= x
Hence, this axiom is verified.


Note: When writing axioms, one should not try to change the language in that axiom. Axioms are predefined statements and their words should not be altered. The other axioms of Euclid are-
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.