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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

  1. 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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  2. 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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