Section 2-3: Deductive Reasoning Goal 2.01: Use logic and deductive reasoning to draw conclusions and solve problems.

Homework: P 78 ( 2 – 22 even): overhead transparency Practice 2-2: Overhead transparency Warm up: Check Skills, p 82 (turn in for a grade) Then begin: If-Then, Converses (back of Practice 2-2) If time: p 81: 55 – 69 all (mixed review) due Friday

Essential Question How are the Law of Detachment and Law of Syllogism used to draw conclusions?

deductive reasoning the process of reasoning logically from given statements to a conclusion.

Two Column Proofs Statements 1. 2. 3. 4. Example on page 90: example 1 top of page Reasons Given 2. Use definition, theorem or postulate

Paragraph Proof Flow Chart Proofs Example on page 98: example #3 bottom of page Flow Chart Proofs Example on page 123: example 1 middle of page

Law of Detachment A law of deductive reasoning that allows you to state a conclusion when a conditional and its hypothesis are both true; the conclusion must be true also. In symbolic form: If p  q is a true statement and p is true, then q is true.

Example If M is the midpoint of a segment, then it divides the segment into two congruent segments. M is the midpoint of AB. Conclude: M divides AB into 2 congruent parts.

Law of Syllogism A law of deductive reasoning that allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement. In symbolic form: If p  q and q  r are true statements, then p  r is a true statement.

Example If a number is prime, then it does not have repeated factors. If a number doesn’t have repeated factors then it is not a perfect square. Conclude: If a number is prime, it is not a perfect square.

How do you think Law of Detachment relates to Venn Diagrams for drawing conclusions? How is Law of Syllogism similar to the Transitive Property? Examples: Worksheet 2-3 Together: 1- 13, odds Students: 2 – 12, evens

Classwork: With partner: p 86 ( 27 -31) Practice 2-3 worksheet: 2 – 12 even Go over.

Individually Practice 2-3: 1 – 11 odds

Additional Examples If a quadrilateral is a square, then it contains four right angles. If a quadrilateral contains four right angles, then it is a rectangle. Draw a conclusion using Law of Syllogism.

If the circus is in town, then there are tents at the fairground If the circus is in town, then there are tents at the fairground. If there are tents at the fairground, then Paul is working as a night watchman. The circus is in town. Use the Laws of Detachment and Syllogism to draw a possible conclusion.

Homework: Checkpoint Quiz 1: p 88 Standardized Test Prep: p 87 (34 – 37) Mixed Review: p 87 (38 – 44) Also don’t forget: Mixed Review p 81 (55 – 69) due Friday