Question

1. given: \\( \overline { b c } \cong \overline { d c } , \overline { a c } \cong \overline { e c } \\) prove: \\( \triangle a b c \cong \triangle e d c \\)

Explanation:

Step1: Vertical angles are equal

$\angle BCA=\angle ECD$

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

Given $BC\cong DC$, $AC\cong EC$, and $\angle BCA=\angle ECD$. So, in $\triangle ABC$ and $\triangle EDC$, we have two sides and the included angle equal.

Answer:

By the Side - Angle - Side (SAS) congruence criterion, $\triangle ABC\cong\triangle EDC$ because $BC\cong DC$, $\angle BCA=\angle ECD$ (vertical angles), and $AC\cong EC$.