In other words, the greatest side of a triangle will be directly opposite of the greatest angle of a triangle.

1) We have triangle ABC, where side AC is greater than side AB. [br][br]2) We then say that angle ABC is also greater than angle ACB.[br][br]3) Since side AC if greater than side AB, let segment AD be made to equal length of AB. (I. 3)[br][br]4) Let BD be joined to create a segment.[br][br]5) Since angle ADB is an exterior angle of the newly created triangle BCD, it is greater than the interior and opposite angle DCB. (I. 16)[br][br]6) We also have that angle ADB is equal to ABD, as side AB is equal to side AD. [br][br]7) Thus, angle ABD is also greater than angle ACB.[br][br]8) Thus, angle ABC is also greater than angle ACB.[br][br]Done.