Question

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

Explanation:

Step1: Vertical angles are congruent

$$\angle ACB\cong\angle ECD$$

Step2: Use SAS (Side - Angle - Side) congruence

Since $\overline{BC}\cong\overline{DC}$, $\angle ACB\cong\angle ECD$, and $\overline{AC}\cong\overline{EC}$, then $\triangle ABC\cong\triangle EDC$ by SAS.

Step3: Corresponding parts of congruent triangles

If $\triangle ABC\cong\triangle EDC$, then $\angle ABC\cong\angle EDC$ (corresponding angles of congruent triangles are congruent).

Answer:

$\angle ABC\cong\angle EDC$ is proved as above.