Question

in the figure, \\(\overline{tv}\\) and \\(\overline{rc}\\) bisect each other. complete the statement.\\(\triangle ter \cong \triangle\\) ______\
options: vec, evc, ecv, vce

Explanation:

Step1: Identify Bisecting Segments

Since \(\overline{TV}\) and \(\overline{RC}\) bisect each other at \(E\), we have \(TE = VE\) and \(RE = CE\).

Step2: Identify Vertical Angles

\(\angle TER\) and \(\angle VEC\) are vertical angles, so \(\angle TER \cong \angle VEC\).

Step3: Apply SAS Congruence

By the Side - Angle - Side (SAS) congruence criterion, in \(\triangle TER\) and \(\triangle VEC\), we have \(TE = VE\), \(\angle TER=\angle VEC\), and \(RE = CE\). So \(\triangle TER\cong\triangle VEC\).

Answer:

A. \(VEC\)