Use polynomial identities to determine Pythagorean triples.
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Ensure that students memorize the following sets of Pythagorean triples: 3-4-5, 5-12-13, and 7-24-25.
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Prove that if $${ x>1}$$, then a triangle with side lengths $${x^2-1}$$, $${2x}$$, and $${x^2+1}$$ is a right triangle.
Algebra II > Module 1 > Topic A > Lesson 10 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A triangle has side lengths of $${(x^2-y^2 )}$$, $${(2xy)}$$, and $${(x^2+y^2 )}$$. Choose values for $$x$$ and $$y$$. Will the resultant three sides be a right triangle? How do you know?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Generate three Pythagorean triples
Describe, algebraically, how you know that$${(x^2-y^2)}$$, $${(2xy)}$$, and $${(x^2+y^2)}$$ will always result in side lengths for a right triangle.