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Geometry is gross, especially when the geometry you are doing has NOTHING to do with math!

In geometry, a counterexample is a specific case or scenario that disproves a conjecture, statement, or proposed theorem. It serves as evidence that the conjecture is not universally true and highlights an exception to the original claim. By presenting a counterexample, mathematicians can show that a general statement does not hold true in all cases, thereby refuting the conjecture.

To construct a counterexample, one must carefully consider the conditions or assumptions of the statement and find a specific instance where those conditions are met, yet the conclusion or claim fails to hold true. This provides a counterexample that contradicts the initial conjecture and demonstrates its inaccuracy.

Counterexamples are valuable tools in mathematics as they challenge assumptions, prompt further investigation, and help refine or reject conjectures. They emphasize the importance of proving statements rigorously and establishing the necessary conditions for a theorem to hold true universally. By finding counterexamples, mathematicians gain a deeper understanding of the limitations and boundaries of various geometric principles and can refine their theories accordingly.

These videos are designed to go over the logical side of geometry. Topics in this video series include…

Conjectures
Theorem
Postulates
Axioms
Inductive reasoning
Deductive reasoning
Conditional statements
Inverse
Converse
Contrapositive
Biconditional
Law of syllogism
Law of detachment
Paragraph proofs
Fill in the blank proofs
Flow proofs
Two column proof’s on segments, angles, triangle congruency, quadrilaterals, and other important theorems and postulates

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: [ Ссылка ]

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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