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D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m∠DEF?

 Jul 9, 2020
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We calculate side lengths by Pythagorean theorem.

\(DE = \sqrt{17}\\ EF = \sqrt{17}\\ DF = \sqrt{34}\)

 

Obviously, \(DE^2 + EF^2 = DF^2\)

 

So by converse of Pythagorean theorem, m∠DEF = 90o.

 Jul 9, 2020

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