Why we need to follow the terms and condition of postulates and theorems

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Postulates are statements that are assumed to be true without proof. Postulates serve two purposes - to explain undefined terms, and to serve as a starting point for proving other statements. Two points determine a line segment. A line segment can be extended indefinitely along a line.

In order to study geometry in a logical way, it will be important to understand key mathematical properties and to know how to apply useful postulates and theorems. A postulate is a proposition that has not been proven true, but is considered to be true on the basis for mathematical reasoning.

Postulates are the fundamental propositions used to prove other statements known as theorems. Once a theorem has been proven it is may be used in the proof of other theorems. In this way, an entire branch of mathematics can be built up from a few postulates.

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