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Honors Geometry

Honors Geometry. Logic: Inductive Reasoning/Conjecture/Counterexamples. Do Now. <ABC and <DBE are supplementary angles. If m<ABC= 2x+12 and m<DBE= 2x+20, what is x? <QRS and <TRV are complementary angles. If m<QRS= 25+x and m<TRV= 2x+2, what is x?. Homework. Struggles? Confusions

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Honors Geometry

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  1. Honors Geometry Logic: Inductive Reasoning/Conjecture/Counterexamples

  2. Do Now • <ABC and <DBE are supplementary angles. If m<ABC= 2x+12 and m<DBE= 2x+20, what is x? • <QRS and <TRV are complementary angles. If m<QRS= 25+x and m<TRV= 2x+2, what is x?

  3. Homework • Struggles? • Confusions • Questions? • ASK ASK ASK!

  4. Note: • What we cover today will NOT be on your test next week.

  5. Definitions • Inductive Reasoning: reasoning based on the patterns you observe.

  6. Examples:

  7. Conjecture • An educated guess based on a pattern.

  8. Example 1: Movie show times are 8:30 AM, 9:45 AM, 11:00 AM, 12:15 PM…… • Example 2: -2, 4, -8, 16, -32……

  9. Example 3: Point P is the midpoint of line NQ • Example Four: <1 and <2 are complementary angles

  10. Definition: • Counterexample: An example that shows that a conjecture is incorrect.

  11. Examples: Example 5: If the name of a month starts with the letter J, it is a summer month. Example 6: You can connect any three points to form a triangle. Example 7: When you multiply a number by 2, the product is greater than the original number.

  12. Practice Problems • Try some on your own/in small groups • As always, if you are ever confused don’t hesitate to call me over!

  13. Exit Ticket • Find a counterexample to the following statements: • All math teachers at BHS are women • All students in geometry have brown hair

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