SOLUTION: `I am struggling with this proof problem.I could really use some assistance. The question is Given: Triangle DGF is isosceles with base DF, angle EGD =~EGF Prove: EG bisects angl

Algebra ->  Geometry-proofs -> SOLUTION: `I am struggling with this proof problem.I could really use some assistance. The question is Given: Triangle DGF is isosceles with base DF, angle EGD =~EGF Prove: EG bisects angl      Log On


   

Question 875706: `I am struggling with this proof problem.I could really use some assistance. The question is
Given: Triangle DGF is isosceles with base DF, angle EGD =~EGF
Prove: EG bisects angle DEF
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle EGD and triangle EGF

angle GDE is congruent to angle EFG . ( since it is an isosceles triangle base angles are equal.)
Angle EGD is congruent to angle EGF ( given)
Side EF is common
so the triangles are congruent.
Therefore angle GED is congruent to angle GEF
But angle DEF is a linear angle
angle GED is equal to GEF = right angle