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Geometry – Lesson 2.1

Geometry – Lesson 2.1. Patterns and Inductive Reasoning. Geometry 2.1 - Notes. Sketch the next figure (4) in the following pattern. Geometry 2.1 - Notes. Sketch the next figure (5) in the following pattern. Geometry 2.1 - Notes. Describe the “pattern” in words.

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Geometry – Lesson 2.1

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  1. Geometry – Lesson 2.1 Patterns and Inductive Reasoning

  2. Geometry 2.1 - Notes • Sketch the next figure (4) in the following pattern.

  3. Geometry 2.1 - Notes • Sketch the next figure (5) in the following pattern.

  4. Geometry 2.1 - Notes • Describe the “pattern” in words. How would you tell a friend how to draw this pattern?

  5. Geometry 2.1 - Notes • Describe the “pattern” in words. • Must state two things: how to start, and how to get the next object from the previous • Ex: Start with one square. Add a new column to the left of the previous square with one more square than the previously added column

  6. Geometry 2.1 – Vocabulary Conjecture: A conjecture is an unproven statement that is based on observations.

  7. Geometry 2.1 – Vocabulary Inductive Reasoning: The process of looking for a pattern, making a conjecture, and verifying the conjecture is true.

  8. Geometry 2.1 – Notes How do you prove a conjecture is true? We must demonstrate or prove that the statement is true for EVERY case.

  9. Geometry 2.1 – Notes How do you prove a conjecture is false? We must find one example which makes the conjecture false.

  10. Geometry 2.1 – Vocabulary Counterexample: A counterexample is an example which shows the conjecture is false.

  11. Geometry 2.1 – Notes Make a conjecture for the following pattern.

  12. Geometry 2.1 – Notes Patterns may also exist in a sequence of numbers. Can you find a conjecture for each pattern? 3, 6, 12, 24, … 20, 15, 10, 5, … 2, 3, 5, 8, 12 …

  13. Geometry 2.1 – Notes Can you find a counterexample for each conjecture? Squaring a whole number and adding one will always be an even number. For any number x, x2 is always larger than x.

  14. Geometry 2.1 – Notes Check for understanding: Write a conjecture for the TOTAL number of objects in each diagram.

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