STAGES IN STRUCTURE OF A THEOREM
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STAGES IN STRUCTURE OF A THEOREM
Practical geometry of Class 8
GENERAL ENUNCIATION:
Proposition of the theorem.
FIGURE:
A figure may be drawn relavant to what is described in general enunciation and it is to be named.
HYPOTHESIS:
The given condition of the theorem are particularly mentioned with respect to the figure.
CONCLUSION:
In this, what is required to be proved is particularly mentioned using the names in the figure, if necessary.
CONSTRUCTION:
In some theorems, the figure drawn as per general enunciation may not be sufficient to proved the theorem. Then, we may be required to add some more details like lines, angles etc. Such additional details drawn is called construction. Of course, this construction part may not be necessary for every theorem.
PROOF:
This is an important stage in establishing a theorem. Here we establish what is required to be prove as mentioned in the conclusion part by logical steps. This chain of steps starts with what is given in the hypothesis. Each step must be supported only by an axiom or by a definition, or by theorems previously proved, but not by any observation or by intuition.
