SOLUTION: I am having a hard time with a proof. The information i have is: Given: Line Segment EG bisects Angle DEF Angle EDG is congruent to angle EFG Prove: triangle DGF is iso

Question 757622: I am having a hard time with a proof. The information i have is:
Given: Line Segment EG bisects Angle DEF
Angle EDG is congruent to angle EFG
Prove: triangle DGF is isosceles
The shape is a large triangle (DGF) with 3 smaller triangles inside. "G" is the label inside the large triangle.
So far i have:
Angle GEF-Angle GED - Given
Angle EDG is congruent to angle EFG- Given
line segment EG is a common- Given from figure
triangle DGE and Triangle GEF are congruent- AAS
DG is congruent to FG - CPCTC
triangle DGF is isosceles- definition of isosceles.

The feedback i received on this home work was:
The proof demonstrates some steps that are useful in reaching the conclusion. Revision is needed to include all the given information and logically connect it to the conclusion. Some of the proof reasons also require revision.
Can anyone help me? please!
Answer by pmatei(79) (Show Source): You can put this solution on YOUR website!
You did not start with what was given. Your first line is the result of EG bisecting angle DEF, you are not given the fact that those two angles are congruent.
Here is the full proof with reasons:
1. Segment EG bisects Angle DEF - Given
2. Angle GEF congruent Angle GED - Angle bisector definition (your former first line)
3. Angle EDG congruent Angle EFG - Given
4. EG = EG - Reflexive property (instead of EG common line)
5. Triangle DEG congruent Triangle FEG - AAS triangle congruency (Comment: Be sure to write the vertices of the triangle in the same order of their measures. Example: if triangle ABC congruent with triangle DEF, I assume angle A congruent with angle D (first letter in each triangle), angle B congruent with angle E (second letter in each triangle), and angle C congruent with angle F (third letter in each triangle). In your case, angle D (triangle DEG) congruent with angle F (triangle FEG) - first letter in each triangle (D in one, F in the other one); angle DEG (or angle E in triangle DEG) congruent with angle FEG (or angle E in triangle FEG) - E is the second letter for both triangles; and angle EGD (or angle G in triangle DEG) congruent with angle EGF (or angle G in triangle FEG) - thus the third letter for each triangle is G.
6. Segment DG congruent Segment FG - CPCTC
7. Triangle DGF is isosceles - Definition of isosceles triangle.
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