Question

t is the midpoint of \\( \overline { s u } \\), \\( \overline { t v } \cong \overline { u w } \\), and \\( \overline { s v } \cong \overline { t w } \\). complete the proof that \\( \triangle s t v \cong \triangle t u w \\).

Explanation:

Step1: Given

Given \( T \) is the midpoint of \( \overline{SU} \), \( \overline{TV}\cong\overline{UW} \), and \( \overline{SV}\cong\overline{TW} \).

Step2: Definition of midpoint

Since \( T \) is the midpoint of \( \overline{SU} \), by the definition of a midpoint, \( \overline{ST}\cong\overline{TU} \).

Step3: SSS (Side - Side - Side) congruence criterion

We have \( \overline{ST}\cong\overline{TU} \) (from step 2), \( \overline{TV}\cong\overline{UW} \) (given), and \( \overline{SV}\cong\overline{TW} \) (given). So, by the SSS (Side - Side - Side) congruence criterion, \( \triangle STV\cong\triangle TUW \).

Answer:

1. Given
2. Given
3. Given
4. Definition of midpoint
5. SSS (Side - Side - Side) congruence criterion