Download 2.3 Apply Deductive Reasoning

Geometry Chapter 2: Reasoning and Proof Section 2.3-­‐ Apply Deductive Reasoning SWBAT: use deductive reasoning to form a logical argument. Common Core: •
G.CO.9, G.CO.10, and G.CO.11  ____________________________________ reasoning uses facts, definitions, accepted properties, and the laws of logic to form a logical argument. Law of Detachment  If the hypothesis of a true conditional statement is true, then the conclusion is _____________________ _____________________. Example 1: Use the Law of Detachment to make a valid conclusion in the true situation, a) If two angles are right angles, then they are congruent. ∠𝐶 𝑎𝑛𝑑 ∠𝐷 are right angles. b) If Nathan is enrolled at Metro High School, then Nathan has an ID number. Nathan is enrolled at Metro High School. Geometry Chapter 2: Reasoning and Proof Example 2: Use the Law of Syllogism If possible, use the Law of Syllogism to write a new conditional statement from the pair of two statements. a) If the radius of a circle is 4ft, then the diameter is 8ft. If the radius of a circle is 4ft, then its area is 16𝜋𝑓𝑡 ! . b) If Joe takes Geometry this year, then he will take Algebra 2 next year. If Joe takes Algebra 2 next year, then he will graduate. c) If 𝑦 ! = 8, 𝑡ℎ𝑒𝑛 𝑦 = 2. 𝐼𝑓 𝑦 = 2, 𝑡ℎ𝑒𝑛 3𝑦 + 4 = 10. Example 3: Use inductive and deductive reasoning What conclusion can you make about the product of two odd numbers? Geometry Chapter 2: Reasoning and Proof Example 4: Reasoning from a Graph Tell whether the statement is a result of inductive reasoning or deductive reasoning. Explain your answer. a) A 120-­‐pound person uses twice as many calories when cycling 4 hours than when cycling 2 hours. b) The 120-­‐pound person uses fewer calories per hour the longer he or she cycles. Homework: Practice 2.3 A