Question

t is the midpoint of (overline{su}). complete the proof that (\triangle tuwcong\triangle tsv).

statement	reason
2	(overline{uw}congoverline{sv})	given
3	(overline{tv}congoverline{tw})	given
4	(overline{st}congoverline{tu})	definition of midpoint
5	(\triangle tuwcong\triangle tsv)

Explanation:

Step1: Recall the SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the sides of the triangles

In \(\triangle TUW\) and \(\triangle TSV\):

• We know that \(\overline{UW}\cong\overline{SV}\) (given)
• \(\overline{TV}\cong\overline{TW}\) (given)
• \(\overline{ST}\cong\overline{TU}\) (definition of mid - point)

Answer:

By the SSS (Side - Side - Side) congruence criterion.