**Axioms or postulates are the assumptions which are obvious universal truths. They are not proved.**

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

For example:

Draw a line segment AB of length 10cm. Draw a second line CD having length equal to that of AB, using a compass. Measure the length of CD. We see that, CD = 10cm.

We can write it as, CD = AB and AB = 10cm implies CD = 10cm.

**Axiom 2: If equals are added to equals, the wholes are equal.**

Suppose we have two line segments AB and DE of equal length. Add BC to AB and add EF to DE. If BC = EF, then AC = DF.

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

Suppose we have two line segments of equal length. Remove BC from AC and EF from DE respectively. If BC = EF, then AB = DE.

**Axiom 4: Things which coincide with one another must be equal to one another.**

This means that if two geometric figures can fit completely one in to another, they are essentially the same.

**Axiom 5: The whole is greater than the part.**

Take a container of water. Remove some water from it. Will the remaining volume of water the same as the original volume?

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