Both inductive reasoning and deductive reasoning are used in mathematics, particularly in writing proofs. You have already practiced identifying the difference between induction and deduction, an you have written scenarios describing situations that requires one of the two methods of reasoning. On this page, you'll need to think about what is similar and different about the two approaches. The table below should help you compare and contrast.
| Inductive Reasoning | Collect data. Find a pattern. Generalize the pattern into a statement. |
| Deductive Reasoning | Identify the two parts of the conjecture you wrote or were given: the hypothesis and the conclusion. Use the rules of logic and your knowledge of geometry to create a new conditional statement. |
Now see if you can identify the type of reasoning used by each of these students to solve a problem.
Carmen
Sasha
Carmen knows that a midpoint, by definition, cuts a line segment into two congruent line segments. She also knows that if two line segments are congruent, then they have the same measure. Carmen makes the new conjecture that the midpoint of a line segment makes two line segments of the same measure.
What kind of logical reasoning did Carmen use?
deduction
After seeing the number pattern -5, -3, -1, 1, 3..., Sasha decides that she can make this conjecture To create or continue this pattern, you start at -5 and add 2.
What kind of logical reasoning did Sasha use?
Sasha used inductive reasoning.
Question
What do the approaches used by Carmen and Sasha have in common?
