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Geometry Notes

Geometry Notes. Section 2-1 9/20/07. What you’ll learn. How to make conjectures based on inductive reasoning How to find counterexamples. Vocabulary . Conjecture Inductive reasoning Counterexample. Conjecture. An educated guess. Make a conjecture.

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Geometry Notes

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  1. Geometry Notes Section 2-1 9/20/07

  2. What you’ll learn • How to make conjectures based on inductive reasoning • How to find counterexamples

  3. Vocabulary • Conjecture • Inductive reasoning • Counterexample

  4. Conjecture • An educated guess

  5. Make a conjecture • Given: lines land m are perpendicular • Conjecture: lines land m form adjacent angles • Conjecture: lines land m form right angles • Conjecture: lines land m form congruent, adjacent angles

  6. Inductive Reasoning • An argument using many examples to support the conjecture

  7. Counterexamples • A false example • An example that contradicts the statement

  8. Use inductive reasoning to find the next two terms in each sequence. • 4, 8, 12, 16, _____, _____ • 400, 200, 100, 50, 25, _____, _____ • 1/8, 2/7, ½, 4/5, _____, _____ • -5, 3, -2, 1, -1, 0, _____, _____ • 360, 180, 120, 90, _____, _____ • 1, 3, 9, 27, 81, _____, _____ • 1, 5, 17, 53, 161, _____, _____ • 1, 5, 14, 30, 55, _____, _____ 24 20 12.5 6.25 5/4 2 -1 -1 72 60 729 243 485 1457 91 140

  9. True or False? If false give a counter example. . . • Given: m + y > 10, y > 4 • Conjecture: m< 6 • Try a number for m that would contradict your conjecture • Conjecture: m< 6 so let’s try m = 7 • 7 + 4* > 10 *remember: y > 4 • 11> 10 • Is a true statement so our conjecture is false.

  10. M P A True or False? If false give a counter example. . . • Given: AM = MP • Conjecture: M is the midpoint of AP • What might a counterexample look like? • Does it say M is between A and P? • No • Given AM = MP, M is not always the mdpt of AP

  11. True or False? If false give a counter example. . . • Given: A(-4, 8), B(3,8), C(3, 5) • Conjecture: ΔABC is a right triangle • How would you know if it is a right triangle? • Use the distance formula to find AB, BC, and AC • Then see if those measures work in the pythagorean theorem

  12. True or False? If false give a counter example. . . • Given: noncollinear points R, S, and T • Conjecture: RS, ST, and RT form a triangle • Through any two points there is a unique line • RS, ST, and RT would have to make a triangle

  13. Have you learned? • How to make conjectures based on inductive reasoning? • How to find counterexamples? • Assignment P. 64 (11-67odd) & Notes 2-2

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