Question

decide whether enough information is given to prove that the triangles are congruent. if so, state the theorem you can use.

△rsv, △utv

Explanation:

Step1: Identify vertical angles

$\angle RVS$ and $\angle UVT$ are vertical angles. By the vertical angles theorem, $\angle RVS=\angle UVT$.

Step2: Check for congruent angles and sides

We are given that $\angle S=\angle T$ (marked in the figure) and $VS = VT$ (marked in the figure).

Step3: Apply the ASA (Angle - Side - Angle) congruence theorem

In $\triangle RSV$ and $\triangle UTV$, we have $\angle S=\angle T$, $VS = VT$, and $\angle RVS=\angle UVT$. So, by the ASA (Angle - Side - Angle) congruence theorem, $\triangle RSV\cong\triangle UTV$.

Answer:

Yes, enough information is given. The ASA (Angle - Side - Angle) congruence theorem can be used to prove that $\triangle RSV\cong\triangle UTV$.