SOLUTION: Statements Reasons DGF triangle is isosceles with base DF GIVEN EGD angle is congruent to EGF angle GIVEN EG segm

Question 935534: Statements Reasons
DGF triangle is isosceles with base DF GIVEN
EGD angle is congruent to EGF angle GIVEN
EG segment is congruent to EG segment Reflexive Property
DG is congruent to FG GIVEN
FGE triangle is congruent to triangle EGD SAS
DEG angle is congruent to FEG angle CPCTC
Segment EG bisects DEF angle Angle Bisector Definition
My problem is I can not have a reason of GIVEN for step 4 but all other steps are correct not sure what I'm missing?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
apparently you were not given that GD is congruent to GF.
but you are given that the triangle is isosceles, and you are given that angle EGD is congruent to angle EGF.
you are also given that DF is the base.
the base angles of the triangle therefore have to be DEG and EFG because one sides of each of those angle is the base.
since the triangle is isosceles, then the base angles must be congruent because that is one of the properties of an isosceles triangle.
since the triangle is isosceles, then the sides opposite the base angles must also be congruent because that is also one of the properties of an isosceles triangle.
without getting too deep into it, i would say a simpler reason might be:

DG is congruent to FG (By definition, an isosceles triangle is a triangle that has two equal sides and a third side, which is called the base).
you might also be able to shorten this to (definition of an isosceles triangle), but that may be too cryptic although i have seen other proofs that sometimes use shorter explanations such as that.

it follows from the fact that you are given that the triangle is isosceles, and you are given that the base of the triangle is DF.

that means that the two congruent sides must be DG and FG.

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