SOLUTION: Please help me solve this proof: Prove that if a line is drawn through the vertex of an isosceles triangle parallel to the base, it bisects the exterior angle at the vertex.

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Question 912739: Please help me solve this proof:
Prove that if a line is drawn through the vertex of an isosceles triangle parallel to the base, it bisects the exterior angle at the vertex.
I have drawn the picture as the question states, but am not sure how to prove that the line bisects the exterior angle with steps using a proof.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

Let ABC be the triangle
AE is drawn parallel to BC
CAF is the external angle
To prove AE bisects CAF
AE is parallel to BC and AC is the transversal
So angle CAE = ACB ( alternate angle test)
AE is parallel to BC and Bf is the transversal
so EAF = ABC ( corresponding angles test)
But ABC = ACB ( isosceles triangle)
therefore EAF = CAE