Final answer:
A student should use a deductive proof to demonstrate that the base angles of an isosceles triangle are congruent, since this type of reasoning is grounded in established geometric definitions and principles.
Step-by-step explanation:
To prove that the base angles of an isosceles triangle are congruent, a student should use a deductive proof. Deductive reasoning starts with a general statement, or hypothesis, and examines the possibilities to reach a specific, logical conclusion. In geometry, this involves starting with known definitions, postulates, and previously proven theorems to establish the truth of a given proposition.
In proving the congruence of base angles in an isosceles triangle, one would reference the fact that in an isosceles triangle, there are two sides with equal length (the legs). By the definition of isosceles triangles and the congruent sides property, one can deduce that the angles opposite those sides are also congruent. Therefore, we use deductive reasoning to reach a logical conclusion based on geometric principles. An inductive proof, on the other hand, would rely on observing patterns and making a conjecture, which is not suitable for a geometric proof that requires a definite conclusion. Geometric and algebraic proofs are methods in which deductive reasoning is applied, but the most appropriate term here is a deductive proof.