Exterior Angle Bisector Theorem

Theorem
An angle bisector of an exterior angle of a triangle divides the opposite side externally into segments proportional to the adjacent sides.
Setup for Proof
Given: [math]\overline{AD}[/math] bisects the exterior angle of [math]\triangle ABC[/math] at [math]A[/math].[br][br]Prove: [math]\frac{DB}{DC}=\frac{AB}{AC}[/math][br][br]Construction:[br]Construct [math]\overline{BE}[/math] parallel to [math]\overline{AD}[/math] through [math]B[/math], intersecting [math]\overline{AC}[/math] at [math]E[/math]
Explore
Move [math]A[/math] to change the type of triangle for [math]\triangle ABC[/math].
Will the angle bisector always intersect [math]\overleftrightarrow{BC}[/math]?
Fechar
– Brian Sterr

Informação: Exterior Angle Bisector Theorem