Deductive Reasoning Geometry Chapter 2-3 Mr. Dorn

2-3 Deductive Reasoning Deductive Reasoning: Law of Detachment: Reasoning based on patterns and logic. When a conditional statement is considered true and the hypothesis is satisfied, then we can state that the conclusion will also be satisfied. Ex. 1: If a vehicle is a car, then it has four wheels is a true conditional. A sedan is a car. Use the Law of Detachment to reach a valid conclusion. A sedan has four wheels.

2-3 Deductive Reasoning Ex. 2: Determine if a valid conclusion can be reached from the two true statements. (1)If I watch TV, I will not do my homework. (2)I did my homework. No valid conclusion can be made because it is not given that the hypothesis has been satisfied.

2-3 Deductive Reasoning Law of Syllogism: When two conditional statements are considered true and the conclusion in one statement is the hypothesis in the second statement, a third conditional can be made using the hypothesis of the first statement and the conclusion of the second. Ex. 3: Write a true conditional using the Law of Syllogism and the following true statements. If it is a Nok sculpture, then it has hollowed-out eyes and mouth. If a sculpture has hollowed-out eyes and mouth, then it has air vents that prevent it from cracking. If it is a Nok sculpture, then it has air vents that prevent it from cracking.

2-3 Deductive Reasoning Ex. 4: Determine if a valid conclusion can be reached from the two true statements using the Law of Syllogism. (1)If Elena takes the car to the store, she will stop at the post office. (2)If Elena stops at the post office, she will buy stamps. If Elena takes the car to the store, she will buy stamps.

2-3 Deductive Reasoning Ex. 5: Determine if statement (3) is a valid conclusion derived from statements (1) and (2). If it does, state which law was used. (1)Vertical angles are congruent. (2). (3) and are vertical. Invalid conclusion.