Question

1. given: ∠s ≅ ∠u, and \\(\overline{tr}\\) bisects ∠stu

prove: \\(\triangle srt \cong \triangle urt\\)

Explanation:

Step1: State given congruent angles

$\angle S \cong \angle U$

Step2: Use angle bisector definition

Since $\overline{TR}$ bisects $\angle STU$, $\angle STR \cong \angle UTR$

Step3: Identify common side

$\overline{TR} \cong \overline{TR}$ (Reflexive Property of Congruence)

Step4: Apply AAS congruence rule

Two angles and a non-included side of $\triangle SRT$ are congruent to the corresponding parts of $\triangle URT$, so $\triangle SRT \cong \triangle URT$ by AAS (Angle-Angle-Side) Congruence.

Answer:

$\triangle SRT \cong \triangle URT$ is proven by the AAS Congruence Theorem.