Questions: Use the given information to prove that triangle DEG is congruent to triangle FGE. Statement Reason 1 Reason?

Use the given information to prove that triangle DEG is congruent to triangle FGE. Statement Reason 1 Reason?
Transcript text: Use the given information to prove that $\triangle D E G \cong \triangle F G E$. Statement Reason 1 $\square$ Reason?
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Solution

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Solution Steps

Step 1: Identify given information

We are given two triangles, $\triangle DEG$ and $\triangle FGE$. The segments DE and FG intersect at a point.

Step 2: Identify congruent angles

The angles $\angle DEG$ and $\angle FGE$ are vertical angles, therefore they are congruent. $\angle DEG \cong \angle FGE$.

Step 3: Identify congruent sides

The diagram shows that segment EG is shared by both triangles, so $EG \cong EG$ by the reflexive property.

Final Answer

It is not possible to prove $\triangle DEG \cong \triangle FGE$ with only the provided information. We have one pair of congruent angles and one pair of congruent sides. We need either another pair of angles or another pair of sides to prove congruence using either ASA, AAS, or SAS. The given information is insufficient.

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