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Geometry Notes
Section 2-1
9/20/07
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What you’ll learn
How to make conjectures based on inductive reasoning
How to find counterexamples
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Vocabulary
Conjecture Inductive reasoning Counterexample
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Conjecture
An educated guess
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Make a conjecture Given: lines l and m are
perpendicular
Conjecture: lines l and m form adjacent angles
Conjecture: lines l and m form right angles
Conjecture: lines l and m form congruent, adjacent angles
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Inductive Reasoning
An argument using many examples to support the conjecture
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Counterexamples
A false example An example that contradicts the
statement
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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, _____, _____
20 2412.5 6.25
5/4 2
-1 -172 60
243 729485 1457
91 140
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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.
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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
A P
M
Given AM = MP, M is not always the mdpt of AP
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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 ACThen see if those measures work in the pythagorean theorem
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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
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Have you learned?
How to make conjectures based on inductive reasoning?
How to find counterexamples?
Assignment P. 64 (11-67odd) & Notes 2-2