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.