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Name: _________________________ Date: _______________ Core-Geo: 2.1 Inductive Reasoning Warm-up: 1. Solve for x: 8 – 3x = -7 2. Simplify: 8x2 – 8x + 3 – x – 10 + 15x2 + 3x3 3. Simplify: 3(x + y2) + 5(y2 – 5x) + x 1.5 Review 1. Draw a pair of complementary angles. 2. Draw two angles that form a linear pair. 1 2.1 Use Inductive Reasoning Vocabulary Conjecture _________________________________________________________________ _______________________________________________________________________ Inductive Reasoning _________________________________________________________________ _______________________________________________________________________ Counterexample _________________________________________________________________ _______________________________________________________________________ Example 1: Describe a visual pattern (a) Describe how to sketch the fourth figure in the pattern. Then sketch the fourth figure. Each rectangle is divided into _______ as many equal regions as the figure number. Sketch the fourth figure by dividing the rectangle into __________. Shade the section just ________ the horizontal segment at the _______. (b) Sketch the fifth figure in the pattern. Three dots (…) tell you that the pattern continues. Example 2: Describe the number pattern (a) Describe the pattern in the numbers –1, –4, –16, –64, …. Notice that each number in the pattern is ________ times the previous number. –1, –4, –16, –64, … × ___ × ___ × ___ × ___ (b) Write the next three numbers in the pattern. 2 Example 3: Make a conjecture Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of the points. Make a table and look for a pattern. Notice the pattern in how the number of connections ___________. You can use the pattern to make a conjecture. 1 2 3 4 ____ ____ ____ ____ Number of points 5 • Picture Number of connections +___ +___ +___ ____ +____ Conjecture You can connect five noncollinear points _____ different ways. Example 4: Find a counterexample A student makes the following conjecture about the difference of two numbers. Find a counterexample to disprove the student’s conjecture. Conjecture The difference of any two numbers is always smaller than the larger number. To find a counterexample, you need to find a difference that is ____________ than the ____________ number. _____– _____ = _____ Because_____ _____, a counterexample exists. The conjecture is false. Hmwk #7 p. 75 # 3, 5, 7, 11, 13, 30, 40 3