Theorem 8-4
In ∆ABC, if c^2 < a^2 + b^2,
then ∠C < 90
and ∆ABC is acute.
This is after teaching Pythagorean Theorem.
The first piece is easy to prove. If two triangles have two sides same, the one with larger angle between them has longer third side. Just compare with the second triangle with c^2 = a^2 + b^2, we see ∠C < 90.
The second conclusion seems not true. We can pick b = 1, a=101, and c = 100.5
All conditions satisfied. But ∠B > 90.
Do I missing anything? Thanks.
This book is "Geometry written by "McDougal Littell".
