Question

prove that \\( \triangle t u v \cong \triangle t w v \\).

Explanation:

Step1: Identify the common side

$\overline{TV}\cong\overline{TV}$ (Reflexive property of congruence)

Step2: Use the given congruent sides

$\overline{TU}\cong\overline{TW}$ (Given)

Step3: Use the given congruent sides

$\overline{UV}\cong\overline{WV}$ (Given)

Step4: Apply SSS congruence

In $\triangle TUV$ and $\triangle TWV$, we have $\overline{TU}\cong\overline{TW}$, $\overline{UV}\cong\overline{WV}$, $\overline{TV}\cong\overline{TV}$. By the Side - Side - Side (SSS) congruence criterion, $\triangle TUV\cong\triangle TWV$.

Answer:

$\triangle TUV\cong\triangle TWV$ by SSS (Side - Side - Side) congruence.