Question

t is the midpoint of su. complete the proof that \\( \triangle tuw \cong \triangle stv \\).

Explanation:

Step1: Definition of midpoint

If \(T\) is the midpoint of \(\overline{SU}\), then by the definition of a midpoint, it divides the segment \(\overline{SU}\) into two equal parts. So, \(\overline{ST}\cong\overline{TU}\).

Step2: SSS (Side - Side - Side) Congruence Criterion

We have \(\overline{TW}\cong\overline{SV}\) (given), \(\overline{TV}\cong\overline{UW}\) (given), and \(\overline{ST}\cong\overline{TU}\) (from step 1).
By the SSS (Side - Side - Side) congruence criterion for triangles, if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. So, \(\triangle TUW\cong\triangle STV\) because \(ST = TU\), \(TW=SV\), \(TV = UW\).

Answer:

1. Reason: Definition of midpoint
2. Reason: SSS (Side - Side - Side) Congruence Criterion