2.3 Apply Deductive Reasoning

Use deductive reasoning to form a logical argument

Deductive Reasoning

• Uses facts, definitions, accepted properties, and laws of logic to form an argument.

• “Putting two and two together”

• Law of Detachment: If the hypothesis of a true conditional statement is true, then the conclusion is also true.

Example 1: Use the Law of Detachment to make a valid

conclusion1. If two segments have the same length, then

they are congruent. You know that BC = XY.

2. Mary goes to the movies every Friday and Saturday night. Today is Friday.

Guided Practice #1 page 88

Using the Law of Syllogism• When given two if-then statements, take the

hypothesis of the first and pair it with the conclusion of the second. (Note: both original statements have to be true)

• If you take notes in class, you will do better on your homework.

• If you do better on your homework, you will have better grades.

• Using Law of Syllogism: If you take notes in class, you will have better grades.

Important Note About Using the Law of Syllogism

• The conclusion of the one statement must be the hypothesis of the other statement.

Example 2 (in your book)

• Use the law of syllogism to write a new conditional statement. If Rick takes chemistry this year, then Jesse will be Rick’s lab partner.

If Jesse is Rick’s lab partner, then Rick will get an A in Chemistry.

Example 2 (in your book)

• Use the law of syllogism to write a new conditional statement.

If x² > 25, then x² > 20. If x > 5, then x² > 25.

Example 2 (in your book)

• Use the law of syllogism to write a new conditional statement. If a polygon is regular, then all the angles in the interior of the polygon are congruent.

If a polygon is regular, then all of it’s sides are congruent.

Your Turn! GP 2 – 4 page 88

Example 3: Use inductive and deductive reasoning

• What conclusion can you make about the product of an even integer and any other integer?

Extra Example 3

• What conclusion can you make about the product of two odd numbers?

Deciding between Inductive and Deductive Reasoning

• Inductive: You looked at a pattern

• Deductive: You looked at facts, rules, etc., and used simple logic

Example 4 (in your book)Inductive or Deductive, Explain.

Each time Monica kicks a ball up in the air, it returns to the ground. So the next time Monica kicks a ball up in the air, it will return to the ground.

Reptiles are cold-blooded. Parrots are not cold-blooded. Sue’s pet parrot is not a reptile.

Inductive or Deductive

• Whenever it rains in the morning, afternoon baseball games are canceled. The baseball game this afternoon was not canceled. So, it did not rain this morning.

Inductive or Deductive

• Every time Tom has eaten strawberries, he has had a mild allergic reaction. The next time he eats strawberries, he will have a mild allgergic reaction.

Closure Activity

• Create your own example of using the law of syllogism.

Homework

• 1,4-28 (omit 16), 30 – 38 Due Wednesday

Quiz coming up over 2.1 – 2.3!