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Geometry

Geometry. Vocabulary. Conjecture- an unproven statement that is based on observation. Inductive Reasoning- when you find a pattern in specific cases and then write a conjecture for the general case. Deductive Reasoning- Uses facts, definitions, and /or accepted properties

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Geometry

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  1. Geometry

  2. Vocabulary Conjecture- an unproven statement that is based on observation. Inductive Reasoning- when you find a pattern in specific cases and then write a conjecture for the general case. Deductive Reasoning- Uses facts, definitions, and /or accepted properties Counter example- a specific case for which a conjecture is false.

  3. Make and test a conjecture about the product of any two odd integers. Step 1: find a pattern using a few groups of small numbers

  4. 3 x 13 = 39 7 x 21 = 147 5 x 9 = 45 11 x 9 = 99 Conjecture:

  5. Step 2: Test your conjecture using other numbers. For example, test that it works with pairs 17, 19, and 23, 31.

  6. Make and test a conjecture about the product of any two even numbers.

  7. Make and test a conjecture about the sum of an even integer and an odd integer

  8. Find a counterexample to show that the conjecture is false. Conjecture: All odd numbers are prime. Solution: To find a counterexample, you need to find an odd number that is a composite number.

  9. Find a counterexample to show that the conjecture is false. Conjecture: The difference of two positive numbers is always positive.

  10. Page: red book 217-219 1-21

  11. Conditional Statement- a logical statement that has two parts, a hypothesis ( the if part) and a conclusion ( the then part). p → q Example: If today is Tuesday, then tomorrow is Wednesday. If it is 12:01 pm, then I am hungry.

  12. Converse- formed by switching the hypothesis and the conclusion. q → p If tomorrow is Wednesday, then today is Tuesday.

  13. Negation- the opposite of the original statement. ~ • Inverse- Negates both the hypothesis and the conclusion. ~p → ~q • If today is not Tuesday, then tomorrow is not Wednesday.

  14. Contrapositive- Switch the hypothesis and conclusion and negate both of them. If tomorrow is not Wednesday, then today is not Tuesday. ~q →~p

  15. Equivalent statements- Two statements that are both true or both false. ****A conditional and its contrapositive are equivalent statement.******** Perpendicular lines- Two lines that intersect to form a right angle.

  16. Biconditional statement- A statement that contains the phrase “if and only if”. • Today is Tuesday if and only if tomorrow is Wednesday. • Tomorrow is Wednesday if and only if today is Tuesday. • Red book page 224-2

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