Use the law of detachment to draw a logical conclusion from the two given statements

In order to win a debate or an argument, you must have sound fact and reasoning as to why you are convinced you are right. It’s not enough to just believe you are right, you have to prove it.

Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)

Therein lies the difference between inductive reasoning and deductive reasoning.

Inductive vs Deductive Reasoning

Inductive reasoning uses patterns and observations to draw conclusions, and it’s much like making an educated guess.

Whereas, deductive reasoning uses facts, definitions and accepted properties and postulates in a logical order to draw appropriate conclusions.

Geometry Logic Statements

There are two laws of logic involved in deductive reasoning:

1. Law of Detachment
2. Law of Syllogism

To better understand these two ideas, let’s take a deeper look.

The Law of Detachment

Law of Detachment Definition

Definition

If p equals q and p is also true. Then q is true.

Example

If a bird is the largest of all birds then it is flightless.
And if an ostrich is the largest living bird.
Then an ostrich is flightless.

The Law of Syllogism

Law of Syllogism Definition

Definition

If p equals q and if q equals r, then p equals r.

Example

If you wear school colors, then you have school spirit.
If you have school spirit, then you feel great.
If you wear school colors, then you feel great.

Using these two logic laws we are able to write conclusions and provide reasons for our statements using more than just intuition but sound fact.

Together we will look at countless examples of how to provide conclusions and reasons for such arguments as:

• Collinear Points
• Congruent Angles
• Angle Bisectors
• And more!

And more importantly, deductive reasoning, is the way in which geometric proofs are written, as Spark Notes nicely states. Consequently, this lesson will introduce the framework for writing a two-column proof that will be used in subsequent lessons.

Deductive Reasoning – Lesson & Examples (Video)

39 min

• Introduction to deductive reasoning
• 00:00:25 – Overview of the laws of detachment and syllogism
• 00:05:09 – Use the law of detachment to determine if the statement is valid (Examples #1-2)
• 00:08:17 – Use the law of syllogism to write the statement that follows (Examples #3-5)
• Exclusive Content for Member’s Only

• 00:13:24 – Use logic to give a reason for each statement (Examples #6-11)
• 00:24:22 – Name the definition used for each conclusion (Examples #12-16)
• 00:30:46 – Draw a conclusion and name the definition used as the reason (Examples #17-19)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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