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

  1. “Whole is greater than part”. This statement is true in physics, chemistry, mathematics, geometry, biology, economics etc.
  2. “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.
  3. “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.
  4. “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.
  5. “Things which are double of same things are equal to one another”. If A= A’ then 2A= 2A’.
  6. “Things which are halves of same things are equal to one another”. If A= A’ then ½ A= ½ A’.
  7. “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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