Geometry! I have a question about the converse of the pythagorean theorem. Please show me how you got the answer too, so I understand the problem. Thank you:) The question states: Match the side lengths with the appropriate description. ___ 1. 26, 20, 17 ___ 2. 26, 20, 14 ___ 3. 26, 10, 24 ___ 4. 26, 10, 15   a. Right Triangle b. Acute Triangle c. Obtuse Triangle d. Not a Triangle   * Pick a letter for each one.*

Expert Answers

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Let `c` represent the longest side of the triangle. `a,b` will represent the other two sides.

(1) side lengths 26,20,17

This is an acute triangle. Here `c^2<a^2+b^2`

(2) side lengths 26,20,14

This is an obtuse triangle. Here `c^2>a^2+b^2`

(3) side lengths 26,10,24

This is a right triangle. Here `c^2=a^2+b^2` (You might also recognize the sides as the multiple of a basic pythagorean triplet -- namely 5-12-13)

(4) side lengths 26,10,15

This is not a triangle. From the triangle inequality theorem we know that the sum of any two sides of a triangle must be longer than the third side. Here 10+15=25<26.

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