On the Triangle Inequalities Worksheet, go back to problems 1-8 and classify the triangle as acute, obtuse, or right using the Pythagorean Theorem, combined with your knowledge of the Hinge Theorem.

The strategy is as follows:

Take your 3 numbers, and pretend they are the sides of a right triangle.  Plug them into the pythagorean theorem (a^2+b^2=c^2) where c is the largest side.  If the numbers work with the pythagorean theorem (the two sides are actually equal), then the triangle must be a right triangle!  If it doesn’t work, focus on the two smaller sides, a and b.  What value of c would make a right triangle?  How does “the c you have” compare to “the c that  you want for a right triangle.”  If “the c you have” is smaller, then that would make the angle across from it smaller than 90 degrees, making the triangle acute.  Thing about what conditions would make a triangle obtuse.




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