GEOMETRY – P7. HONORS GEOMETRY – P4 Bellwork – PSAT Question (C) 30.

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Presentation transcript:

GEOMETRY – P7

HONORS GEOMETRY – P4

Bellwork – PSAT Question (C) 30

INTRO TO GEOMETRY A.Syllabus B.Section 1.1 – Inductive Reasoning

Patterns in Geometry In Geometry, we often have to look at a group of problems or examples to determine what is going on. This process is called Inductive Reasoning. Example: 2, 6, 18, 54 By using inductive reasoning we can determine a pattern…. Multiplying by 3

Patterns in Geometry When we use inductive reasoning our guess at the rule or the pattern is called our conjecture. What are the next two numbers in the pattern? 1, 2, 4, 7, 11, ____, ____ Make a conjecture for the rule in the sequence above. To find the next term, we are adding consecutive integers.

A.Find the next two numbers in the sequence. B.Make a conjecture for each. 1.2, 5, 8, 11,…_____, _____ 2.1/3, 1/6, 1/12, 1/24… _____, _____ 3.4, 44, 444, 4444,… _____, _____ 4.27, 9, 3, 1,…_____, _____ 5.2, 3, 6, 7, 14, 15,…_____, _____

Continued… 1.1, 4, 9, 16, 25,…_____, _____ 2.1, 2, 6, 24, 120,…_____, _____ 3.A, C, E, G, I,…_____, _____ 4.J, F, M, A, M,…_____, _____ 5.1, 1, 2, 3, 5, 8,…_____, _____

Using Inductive Reasoning The following pictures are made of toothpicks. How many toothpicks would it take to made 10 of these boxes in a row? What about 20 boxes?

Using Inductive Reasoning Find the sum of the first 6 even numbers, the first 30 even numbers, and the first 100 even numbers.

Counterexamples Conjectures are not always true. If you believe that someone has made an incorrect conjecture, you can offer a counterexample to show they are wrong. For Example: Conjecture: Whenever you add two numbers together the answer is always bigger than the two numbers you added. (This is not always true) Counterexample: ???

Homework P 6 (1-11 odd, 26-28, all)