Question

complete the proof that \\( \angle u \cong \angle t \\).

Explanation:

Step1: Identify the triangles

We have \(\triangle STU\) and \(\triangle SUT\).

Step2: Check for congruence

• Statement 1: \(SU\cong ST\) (Given)
• Statement 2: \(\angle S\cong\angle S\) (Reflexive Property of Congruence)
• Statement 3: \(STU\cong\triangle SUT\) (SAS - Side - Angle - Side Congruence Criterion. The side \(SU = ST\) (from statement 1), the included angle \(\angle S\) is common (statement 2), and \(SU = ST\) (statement 1) again. Wait, no, actually, we have two sides \(SU = ST\) (given) and \(SS\) (common side) and the included angle \(\angle S\). So \(\triangle STU\cong\triangle SUT\) by SAS)
• Statement 4: \(\angle U\cong\angle T\) (CPCTC - Corresponding Parts of Congruent Triangles are Congruent)

Answer:

1. Given
2. Reflexive Property of Congruence
3. SAS (Side - Angle - Side)
4. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)