Question

what is the missing statement in the proof? statement reason 1. ∠txu ≅ ∠tvs 1. given 2. ∠stv ≅ ∠utx 2. reflex. prop. 3. △stu is an equilateral triangle 3. given 4. st ≅ ut 4. sides of an equilat. △ are ≅ 5. ? 5. aas 6. ux ≅ sv 6. cpctc ○ △sxu ≅ △tvs ○ △uvx ≅ △sxv ○ △swx ≅ △uwv ○ △tux ≅ △tsv

Explanation:

Step1: Recall 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:

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