Is inductive or deductive reasoning the best way to approach a geometric proof?

Answer 1

Please remember proof gives absolute truth, which means it HAS to be true for all cases satisfying the condition. Hence, inductive reasoning will NEVER be able to be used for that ---- it only supposes that the OBSERVED is true than the rest must, that's garbage, if it's observed of course it's true (in Math), no one knows what will come next. But it's a good place to start, inductive reasoning gives a person incentive to do a full proof.

Do NOT confuse inductive reasoning with inductive proof.

Inductive reasoning: If a1 is true, a2 is true, and a3 is true, than a4 should be true.

Inductive Proof: If a1 is true (1), and for every an, a(n+1) is true as well (2), then,

since a1 is true (1), then a2 is true (2), then a3 is true (2).

You see, in inductive proof, there is a process of deductive reasoning ---- proving (1) and (2). (1) is usually, just plugin case 1. (2) provides only a generic condition, asking you to derive the result (a (n+1) being true), that is deductive reasoning.

In other words, proof uses implications a cause b, and b cause c hence a cause c.

Inductive says though a causes c because I saw one example of it.