Question

Tell whether the reasoning process is deductive or inductive.

By using the definitions of equilateral triangle (a triangle with three congruent sides) and of perimeter (the sum of the lengths of the sides of a figure), Katie concludes that the perimeter of every equilateral triangle is three times the length of a side.

Short answer

The reasoning process is deductive.

Step-by-step solution

Step 1. Define deductive reasoning

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Step 2. Define inductive reasoning

Inductive reasoning is conclusions based on several past observations.

Step 3. State whether reasoning is inductive or deductive

From the given statement “By using the definitions of equilateral triangle (a triangle with three congruent sides) and of perimeter (the sum of the lengths of the sides of a figure), Katie concludes that the perimeter of every equilateral triangle is three times the length of a side.”, it is clear that the conclusion is based on definition. Since, the conclusion based on accepted statement, thus, this conclusion must be true if hypothesis are true.

Therefore, the reasoning process is deductive.