# Inductive & Deductive Reasoning in Geometry: Definition & Uses Video

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• 0:06 Reasoning
• 0:40 Inductive Reasoning
• 1:24 Deductive Reasoning
• 1:58 As Used in Geometry
• 3:44 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson, and you will learn how important inductive and deductive reasoning is in the field of mathematics, especially when dealing with proofs in geometry. Learn how these two fundamental forms of reasoning give rise to formal theorems.

## Inductive and Deductive Reasoning

Inductive and deductive reasoning are two fundamental forms of reasoning for mathematicians. The formal theorems and proofs that we rely on today all began with these two types of reasoning. Even today, mathematicians are actively using these two types of reasoning to discover new mathematical theorems and proofs. Believe it or not, you yourself might be using inductive and deductive reasoning when you make assumptions about how the world works.

## Inductive Reasoning

Defined, inductive reasoning is reaching a conclusion based off of a series of observations. A conclusion that is reached by inductive reasoning may or may not be valid. An example of inductive reasoning is, for example, when you notice that all the mice you see around you are brown and so you make the conclusion that all mice in the world are brown. Can you say for certain that this conclusion is correct? No, because it is based on just a few observations. However, this is the beginning of forming a correct conclusion, or a correct proof. What this observation has given you is a starting hypothesis to test out.

## Deductive Reasoning

Inductive reasoning typically leads to deductive reasoning, the process of reaching conclusions based on previously known facts. The conclusions reached by this type of reasoning are valid and can be relied on. For example, you know for a fact that all pennies are copper colored. Now, if your friend gave you a penny, what can you conclude about the penny? You can conclude that the penny will be copper colored. You can say this for certain because your statement is based on facts.

## As Used in Geometry

So, how does inductive and deductive reasoning figure into geometry? Well, inductive reasoning is the beginning point of proofs, as it gives you a hypothesis you can test out, similar to what we discussed with the mice. For example, we could observe that all three angles of several pairs of triangles are equal and that each pair of triangles look the same, except that one is bigger than the other. Through inductive reasoning, we can reach the conclusion that if two triangles have angles that all measure the same, then they are similar triangles.

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