In the previous section, you learned that if a2 + b2 = c2, then the triangle is a right triangle. But what happens when a2 + b2 ≠ c2? In this section, you will investigate what that means.

Pythagorean Inequalities

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required.Converse of the Pythagorean Theorem

  1. In the dynamic geometry sketch below, click and drag point B to generate several triangles.
  2. Look at the sample table below. Record the values you observed for a2 + b2 and c2 in a similar table in your notes.
a2 + b2
c2
Type of Triangle
Acute, Right, Obtuse
     
     
     
     

 

Journal Entry:
What relationship between a2 + b2 and c2 will generate an acute triangle? An obtuse triangle? A right triangle? Summarize your findings in a chart, using pictures.