What is Deductive Reasoning ?

Geometry is based on a deductive structure -- a system of thought in which conclusions are justified by means of previously assumed or proved statements. The process of deductive reasoning involves three steps:

Step 1: Start with the given conditions (hypothesis).

Step 2: Use logic, definitions, postulates, or previously proved theorems to justify a sequence of thoughts.

Step 3: State your conclusions.

Example 4 :  Given DABC is an equilateral triangle with three congruent sides A@B@C. After we use logic to supply the correct statements in step 2, we can come to the conclusion (theorem): If all the three sides of a triangle are congruent, then the three angles are congruent.