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HW-2.1 Practice A 2.1, 2.2 & 2.4 Quiz FRIDAY www.westex.org HS, Teacher Websites 9-23-13 Warm up—Geometry CPA Find the next item in the pattern. 1, 5, 9, 13, … GOAL: I will be able to: 1. use inductive reasoning to find patterns and make conjectures. 2. find counterexamples to disprove conjectures. HW-2.1 Practice A 2.1, 2.2 & 2.4 Quiz FRIDAY www.westex.org HS, Teacher Websites Name _________________________ Geometry CPA 2-1 Use Inductive Reasoning to make Conjectures GOAL: I will be able to: 1. use inductive reasoning to find patterns and make conjectures. 2. find counterexamples to disprove conjectures. Date ________ Example 1: Find a Pattern Find the next item in the pattern. January, March, May, ... You Try: Find the next item in the pattern. 1. 7, 14, 21, 28, … 2. 3. 0.4, 0.04, 0.004, … When several examples form a pattern and you assume the pattern will continue, you are applying _______________ ____________. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. You may use inductive reasoning to draw a conclusion from a pattern. A statement you believe to be true based on inductive reasoning is called a __________________. Example 2: Making a Conjecture The sum of two positive numbers is ? . You Try: Complete the conjecture. 1. The number of lines formed by 4 points, no three of which are collinear, is ? . 2. The product of two odd numbers is ? . Example 3: Biology Application Make a conjecture about the lengths of male and female whales based on the data. Average Whale Lengths Length of Female (ft) 49 51 50 48 51 47 Length of Male (ft) 47 45 44 46 48 48 To show that a conjecture is always true, you must prove it. To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a ____________________. A counterexample can be a drawing, a statement, or a number. Inductive Reasoning 1. Look for a pattern. 2. Make a conjecture. 3. Prove the conjecture or find a counterexample. Example 4: Finding a Counterexample Show that the conjecture is false by finding a counterexample. For every integer n, n3 is positive. You Try: Show that the conjecture is false by finding a counterexample. 1. Two complementary angles are not congruent. 2. The monthly high temperature in Abilene is never below 90°F for two months in a row. Monthly High Temperatures (ºF) in Abilene, Texas Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 88 89 97 99 107 109 110 107 106 103 92 89 3. For any real number x, x2 ≥ x. 4. Supplementary angles are adjacent. 5. The radius of every planet in the solar system is less than 50,000 km. Planets’ Diameters (km) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto 4880 12,100 12,800 6790 143,000 121,000 51,100 49,500 2300 EXIT TICKET Name _______________________ 9-23-13 How many counterexamples are necessary to show a conjecture is false? Explain why. EXIT TICKET Name _______________________ 9-23-13 How many counterexamples are necessary to show a conjecture is false? Explain why. EXIT TICKET Name _______________________ 9-23-13 How many counterexamples are necessary to show a conjecture is false? Explain why. EXIT TICKET Name _______________________ 9-23-13 How many counterexamples are necessary to show a conjecture is false? Explain why. EXIT TICKET Name _______________________ 9-23-13 How many counterexamples are necessary to show a conjecture is false? Explain why.
