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Warm Up Over Chapter 1 Find SR if R is the midpoint of SU shown in the figure. A. 22 B. 16 C. 4 D. 0 Chapter 2 Section 1 Take Note Inductive Reasoning Description: using a number of specific examples to arrive at a conclusion Example: 6, 12, 18, 24, …. The conclusion you come up with is called a conjecture Conjecture: Adding 6 to the previous term For Example Patterns and Conjecture A. Write a conjecture that describes the pattern 2, 4, 12, 48, 240. Then use your conjecture to find the next item in the sequence. Step 1 Look for a pattern. 2 4 12 48 240 Step 2 ×2 ×3 Make a conjecture ×4 ×5 The numbers are multiplied by 2, 3, 4, and 5. The next number will be multiplied by 6. So, it will be 6 ● 240 or 1440. Answer: 1440 Patterns and Conjecture For Example B. Write a conjecture that describes the pattern shown. Then use your conjecture to find the next item in the sequence. Step 1 Look for a pattern. 3 9 +6 18 +9 For Example Step 2 Patterns and Conjecture Make a conjecture. Conjecture: Notice that 6 is 3 × 2 and 9 is 3 × 3. The next figure will increase by 3 × 4 or 12 segments. So, the next figure will have 18 + 12 or 30 segments. Answer: 30 segments Check Draw the next figure to check your conjecture. You Try A. Write a conjecture that describes the pattern in the sequence. Then use your conjecture to find the next item in the sequence. A. B. C. D. You Try B. Write a conjecture that describes the pattern in the sequence. Then use your conjecture to find the next item in the sequence. 1 3 6 10 For Example A. Make a conjecture about the product of two odd numbers. Take Note Counterexample Description: a false example. It shows a conjecture cannot be true. Example: If ∠A and ∠B are complementary, then they share a common side. Counterexample: You Try Find Counterexamples Find a counterexample to show this conjecture is false: A. If a ray intersects a segment at its midpoint, then the ray is perpendicular to the segment. Perpendicular = intersects at a right angle Homework • HW 10: Pg.94 #’s 1-8, 12-16, 31, 40, 42