# Honors Geometry Companion Book, Volume 1

2.1.3 Using Deductive Reasoning to Verify Conjectures − Worksheet

Example 1: Does each conclusion use inductive or deductive reasoning? 1. At Bell High School, students must take Biology before they take Chemistry. Sam is in Chemistry, so Marcia concludes that he has taken Biology.

2. A detective learns that his main suspect was out of town the day of the crime. He concludes that the suspect is innocent.

Example 2: Determine if each conjecture is valid by the Law of Detachment. 3. Given: If you want to go on a field trip, you must have a signed permission slip. Zola has a signed permission slip. Conjecture: Zola wants to go on a field trip.

4. Given: If the side lengths of a rectangle are 3 ft and 4 ft, then its area is 12 ft 2 . A rectangle has side lengths of 3 ft and 4 ft. Conjecture: The area of the rectangle is 12 ft 2 .

Example 3: Determine if each conjecture is valid by the Law of Syllogism. 5. Given: If you fly from Texas to California, you travel from the central to the Pacific time zone. If you travel from the central to the Pacific time zone, then you gain two hours. Conjecture: If you fly from Texas to California, you gain two hours.

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