Given: measure of angle D=~ measure of angle F ;
line GE bisects angle DEF
Prove: line DG=~ line FG
=~ is the congruent sign
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2 answers

No one is replying is that the way you have described this problem makes no sense.
What are angles D and F ?
if E to G bisects angle DEF then DEG is congruent to FEG 👍
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Damon 
Perhaps angle D is angle GDE and angle F is angle GFE?
If so
you have two angles the same in the two triangles
DEG = FEG (bisect of DEF)
GDE = GFE given
so DGE = FGE anlges in triangle add to 180, if two are the same so is the third
EG is common to both triangles
so
triangle EDG congruent to EFG angle,side,angle
your two lines are now corresponding sides in congruent triangles 👍
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Damon
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