Problem
Statement Bank Def. of Angle Bisector $A D \cong C D$ Def. of Segment Bisector $C D \cong G H$ Given $\angle T S V \cong \angle T S W$ Transitive Property of Congruence Quadrilateral $A B C D \cong$ QuadrilateralEFGH 1. Given: $\triangle S V T \cong \triangle S W T$ Prove: $\overline{S T}$ bisects $\angle V S W$. \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c||}{ statements } & Reasons \\ \hline 1. $\triangle S V T \cong \Delta S W T$ & 1. \\ \hline 2. & 2. Corresponding parts of congruent \\ & figures are congruent. \\ \hline 3. $\overline{S T}$ bisects $\angle V S W$. & 3. \\ \hline \end{tabular}
Solution
Step 1 ：Given: \(\triangle SVT \cong \triangle SWT\)
Step 2 ：\(\angle VST \cong \angle WST\) because corresponding parts of congruent figures are congruent
Step 3 ：By the definition of an angle bisector, \(\overline{ST}\) bisects \(\angle VSW\)
Step 4 ：Final Answer: \(\boxed{Given \triangle SVT \cong \triangle SWT, it follows that \angle VST \cong \angle WST. Therefore, \overline{ST} bisects \angle VSW. Hence, the statement is proven.}\)
