Inductive reasoning usually called generalization, we given by some examples and try to make generalization from those examples to arrive at our conclusion.

For example you can write the number of factor of each number from 1 to 25. And you will only find that only the quadratic number that has odd number of factor. (4 has 3 factors, 9 has 3 factors, 16 has 5 factors, 25 has 3 factor). Then you extend your sample to 1000 for example, and find the same observation, you then conclude that only quadratic number will have odd number of factor.

in Geometry this inductive reasoning has some weakness :

1. Measurement in geometry can not be done precisely, result is only approximate

2. Each sample should be took care carefully, we need to examine every possibility from the sample

3. We do not give / can not give explanation why conclusion are true, the result comes from our observation through samples

but however, this inductive reasoning is a powerful tool in discovering and making conjecture.

the result of inductive reasoning is called conjecture, it is true conclusion that we draw but we can not give any explanation why the conclusion is true, the result in only probably true.

counterexample is any sample that we can use to prove that generalization taken by inductive reasoning is false