1 / 13

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.

rhea
Download Presentation

Geometry Notes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related