Question

what is the missing statement in the proof?

1. ∠txu ≅ ∠tvs
2. given

1. ∠stv ≅ ∠utx
2. reflex. prop.

1. △stu is an equilateral triangle
2. given

1. (overline{st}) ≅ (overline{ut})
2. sides of an equilat. △ are ≅

1. ?
2. aas

1. (overline{ux}) ≅ (overline{sv})
2. cpctc

△sxu ≅ △tvs
△uvx ≅ △sxv
△swx ≅ △uwv
△tux ≅ △tsv

Explanation:

Step1: Recall the AAS (Angle - Angle - Side) congruence criterion

AAS states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Step2: Identify the triangles and their corresponding parts

We have \(\angle TXU\cong\angle TVS\) (given), \(\angle STV\cong\angle UTX\) (reflexive property), and \(\overline{ST}\cong\overline{UT}\) (sides of an equilateral triangle). The triangles in question are \(\triangle TUX\) and \(\triangle TSV\).

Answer:

\(\triangle TUX\cong\triangle TSV\)