Inductive Reason & Conjecture Section 2.1 -Cameron Pettinato -Olivia Kerrigan.

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Presentation transcript:

Inductive Reason & Conjecture Section 2.1 -Cameron Pettinato -Olivia Kerrigan

Inductive Reasoning  Reasoning that uses a number of specific examples to arrive at a conclusion.

Conjecture  A concluding statement reached using inductive reasoning.  “Educated guess”

When making a conjecture...  You must notice a pattern in the sequence  You must make a conclusion for the sequence based on the pattern you determined

Counterexamples  An example that proves a conjecture to be false.

Counterexamples  When proving a conjecture false, you must formulate a mathematical counterexample to support why the conjecture is false.

Sequence  Increasing: +(addition) and x(multiplication)  Decreasing: -(subtraction) and /(division)

Make a conjecture about the sequences…  1, 2, 3, 5, 8, 13, 21, Addition by previous two numbers  3, -1.5,.75, -.25, 34 Division by …

Make conjectures about the geometric relationship…  <ABC is supplementary to <CBD <ABC + <CBD = 180 degrees AB C D

Make conjectures about the geometric relationship…  Line AB is perpendicular to line CD A B DC <ABD is a right angle (90 degrees) <ABC is a right angle (90 degrees)

Determine whether each conjecture is true or false.  If GH and JK form a right angle, then they are perpendicular. True

 If two of the angles in a triangle are congruent, then the triangles are congruent. False Counterexample

 Supplementary angles are adjacent. False Counterexample

Works Cited  › math  es-and-Counterexamples  ainpage.html