Question

use the given information to prove that \\( \triangle abc \cong \triangle edc \\).
given: \\( \overline { b c } \cong \overline { d c } \\)
\\( \angle b a c \cong \angle d e c \\)

Explanation:

Step1: Identify vertical angles

$\angle ACB=\angle ECD$ (Vertical angles are congruent)

Step2: Apply AAS (Angle - Angle - Side) congruence criterion

In $\triangle ABC$ and $\triangle EDC$, we have $\angle BAC=\angle DEC$ (given), $\angle ACB = \angle ECD$ (vertical angles), and $BC = DC$ (given). By AAS (Angle - Angle - Side) congruence, $\triangle ABC\cong\triangle EDC$

Answer:

$\triangle ABC\cong\triangle EDC$ by AAS (Angle - Angle - Side) congruence.