Assignment 4
Proof that the Angle Bisectors
of the Interior Angles of a Triangle are Concurrent
Prove that the angle
bisectors of the interior angles of a triangle are concurrent.
Given
Triangle ABC with angle bisectors AD, BE, and CF.
By the Angle Bisector Theorem,
, ,
By
the Multiplication Property of Equality,
By
Algebra,
By Ceva’s Theorem, AD, BE, CF are concurrent.