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 conclusion 1.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!