State examples of Euclid's axioms in our daily life.

Take the 5 Euclid’s axioms one by one –

Axiom 1: Things which are equal to the same thing are also equal to one another.

Example: Take a simple example.

Say, Raj, Megh, and Anand are school friends. Raj gets marks equal to Megh’s and Anand gets marks equal to Megh’s; so by the first axiom, Raj and Anand’s marks are also equal to one another.

Axiom 2: If equals are added to equals, the whole is equal.

Example: Say, Karan and Simran are artists and they buy the same set of paint consisting of 5 colors. This means, Karan has 5 color set and Simran to has same 5 color set.

⇒ (Karan’s 5 colour set) = (Simran’s 5 colour set) …(i)

Now, they need the special set of 3 paint brushes each and so they buy it. This means Karan buys 3 paint brushes and Simran too buy the same kind of 3 paint brushes.

⇒ (Karan’s 3 paint brushes) = (Simran’s 3 paint brushes) …(ii)

Add the two equals (i) and (ii), we get

(Karan’s 5 color set) + (Karan’s 3 paint brushes) = (Simran’s 5 colour set) + (Simran’s 3 paint brushes)

⇒ Karan’s 8 paint items = Simran’s 8 paint items

This well proves that even after adding their equals, the whole were equal.

Axiom 3: If equals are subtracted from equals, the remainders are equal.

Example: Shriya and Riya are in the same class. Shriya and Riya both have 3 books each. After the end of their semester, both decide to keep one book to themselves while donating the other 2 books to someone needy.

So, after donating two books each they are left with one book each.

Here, we have proved from real life that if equals are subtracted from equals, the remainders (left outs) are also equal.

Axiom 4: Things which coincide with one another are equal to one another.

Example: This is a general axiom. Say, Aradhna is pasting a paper cut dress onto a sketch was drawn on a sketch pad for her project. It’s obvious that the two things, the sketch and the paper cut dress coincides on each other and hence are eventually equal to one another.

Axiom 5: The whole is greater than the part.

Example: Take an easy example. We know that India has 29 states. The states are obviously parts of India. So, here India is whole and states are part.

Take any one state. I have taken Maharashtra. So, obviously, Maharashtra is smaller than India as a whole.