Question

what is the missing statement in the proof?

statement	reason
2. $\angle stv \cong \angle utx$	2. reflex. prop.
3. $\triangle stu$ is an equilateral triangle	3. given
4. $\overline{st} \cong \overline{ut}$	4. sides of an equilat. $\triangle$ are $\cong$
5. ?	5. aas
6. $\overline{ux} \cong \overline{sv}$	6. cpctc

$\bigcirc$ $\triangle sxu \cong \triangle tvs$
$\bigcirc$ $\triangle uvx \cong \triangle sxv$
$\bigcirc$ $\triangle swx \cong \triangle uwv$
$\bigcirc$ $\triangle tux \cong \triangle tsv$

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 elements for congruence

We are given $\angle TXU\cong\angle TVS$ (Angle 1), $\angle STV\cong\angle UTX$ (Angle 2), and $ST\cong UT$ (Side). The triangles that have these corresponding congruent parts are $\triangle TUX$ and $\triangle TSV$.

Answer:

$\triangle TUX\cong\triangle TSV$