Question

the proof below may or may not be correct. if the proof is incorrect, determine the first step number that is not justified and the reason it is not justified.

given: \\( \overline { a d } \cong \overline { b c } \\) and \\( \angle d \cong \angle c \\).

prove: \\( \angle e a b \cong \angle e b a \\).

step	statement	reason
2	\\( \angle d e a \cong \angle c e b \\)	vertical angles are congruent
3	\\( \triangle a d e \cong \triangle b c e \\)	aas
4	\\( \overline { a e } \cong \overline { b e } \\)	corresponding parts of congruent triangles are congruent (cpctc)
5	\\( \angle e a b \cong \angle e b a \\)	in a triangle, angles opposite of congruent sides are congruent

Explanation:

Step1: Check congruence of triangles

To prove $\triangle ADE\cong\triangle BCE$, we need to verify the AAS (Angle - Angle - Side) criterion.
AAS requires two angles and a non - included side of one triangle to be congruent to the corresponding two angles and non - included side of another triangle.
We are given $\overline{AD}\cong\overline{BC}$ (side), $\angle D\cong\angle C$ (angle), and $\angle DEA\cong\angle CEB$ (vertical angles, angle).

Step2: Analyze the application of AAS

In $\triangle ADE$ and $\triangle BCE$, the side $\overline{AD}$ is opposite to $\angle DEA$ in $\triangle ADE$, and the side $\overline{BC}$ is opposite to $\angle CEB$ in $\triangle BCE$.
For AAS, the side should be non - included. But in the given proof, the side $\overline{AD}\cong\overline{BC}$ is not in the correct position for AAS. The AAS criterion is misapplied here.

Answer:

The first step that is not justified is Step 3. The reason is that the AAS (Angle - Angle - Side) congruence criterion is misapplied. The side used in the AAS is not in the correct non - included position for the given angles.