Class 9 Maths Euclid Geometry | Axioms |

**Axioms:**

Axioms are common notions any discipline, not only restricted to Geometry. These are obvious universal truth. They are statements which are accepted as true.

Some of the axioms are

- “Whole is greater than part”. This statement is true in physics, chemistry, mathematics, geometry, biology, economics etc.
- “Things which are equal to same thing are equal to each other”. g. if A=B & C=B. that is both A & C are equal to B, then A & C will be equal.
- “If equals are added to Equals, whole are equal”. E.g. it is known than two glass A & A’ has same volume of water. Now we add equal quantity of water B, to both glass A & A’, then the final volume of water in the jar will be same. A+ B will be equal to A’ + B.
- “If equals are subtracted from Equals, then remainders are equal”. E.g. it is known than two glass A & A’ has same volume of water. Now we remove equal quantity of water B, from both glass A & A’, then the final volume of water in the jar will be same. A- B will be equal to A’ - B.
- “Things which are double of same things are equal to one another”. If A= A’ then 2A= 2A’.
- “Things which are halves of same things are equal to one another”. If A= A’ then ½ A= ½ A’.
- “Things that coincide with one another are equal to one another”. E.g. if two triangles coincide with each other then they are equal.

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