Question

tv ≅ tu. complete the proof that △tuv ≅ △tvu.

1 tv ≅ tu given
2
3

Explanation:

Step1: Identify the common side

In \(\triangle TUV\) and \(\triangle TVU\), \(\overline{TV}\) is common. So, \(\overline{TV}\cong\overline{TV}\) (Reflexive property of congruence: Any segment is congruent to itself).

Step2: Use SSS (Side - Side - Side) congruence criterion

We know that \(\overline{TV}\cong\overline{TU}\) (given), \(\overline{TV}\cong\overline{TV}\) (from step 1), and \(\overline{UV}\cong\overline{VU}\) (Reflexive property of congruence).
By SSS (if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent), \(\triangle TUV\cong\triangle TVU\).

Answer:

Statement	Reason
2. \(\overline{TV}\cong\overline{TV}\)	Reflexive property of congruence
3. \(\triangle TUV\cong\triangle TVU\)	SSS (Side - Side - Side) congruence criterion