9.2 The Converse and Classifying Triangles

Notes

The converse lets you test whether a triangle is right. Let $c$ be the longest side.

• If $a^2 + b^2 = c^2$, the triangle is right.
• If $a^2 + b^2 > c^2$, the triangle is acute.
• If $a^2 + b^2 < c^2$, the triangle is obtuse.
• First check the Triangle Inequality: $a + b > c$.
• Example: 5, 8, 10. $25 + 64 = 89 < 100$, so the triangle is obtuse.