If you look at the various triangles you made during the first part of the lesson you can observe that some of the triangles appear to be acute, some right, and some obtuse.

1. First pick out the triangle that you think looks like a right triangle. We know that the Pythagorean Theorem states that if , where a and b are the two shorter sides, then the triangle is a right triangle. Find the triangle that is a right triangle by checking to see where .

2. If you think other triangles might be a right triangle check to see if for those triangles.

3. If then the triangle is either an acute triangle or an obtuse triangle. First choose those triangles from the pictures that you can definitely classify as acute. How does compare with in the triangles that are definitely acute triangles?

Write a statement that you could use to classify a triangle as an acute triangle.

4. Next pick some triangles that appear to be obtuse. How does compare with in the triangles that are definitely obtuse triangles?

Write a statement that you could use to classify a triangle as an obtuse triangle.

5. Take the rest of the triangles and find out how compare with in the triangles to classify them as acute or obtuse.

6. Describe three numbers larger than 6 that could be used to form an acute triangle.

7. Describe three numbers larger than 6 that could be used to form an obtuse triangle.

8. Describe three numbers larger than 6 that could be used to form a right triangle.

An alternate way to look at this data is to set up three lists L1, L2, and L3 with the three sides and have the calculator find in L4 and in L5. Then by observation answer the questions above.