Question

pick the correct congruence statement

Explanation:

Step1: Analyze the congruent triangles

In congruent triangle statements, the order of the vertices matters. We need to check the corresponding sides and angles.

Step2: Check each option

• For $\triangle VUT\cong\triangle UVE$: The side - angle - side (SAS) or other congruence criteria do not match as per the figure's markings.
• For $\triangle TUV\cong\triangle EUV$: Let's assume the markings in the figure. If we consider the sides and angles, if $TV = EV$ (marked as equal), $UV$ is common, and $\angle TUV=\angle EUV$ (marked as equal), then by SAS (Side - Angle - Side) congruence criterion, $\triangle TUV\cong\triangle EUV$.
• For $\triangle TUV\cong\triangle UEV$: The order of vertices does not follow the congruence criteria based on the figure's markings.
• For $\triangle UTV\cong\triangle EUV$: The side - angle relationships do not match the congruence rules.

Answer:

$\triangle TUV\cong\triangle EUV$