Question

uv ≅ st and tu ≅ sv. complete the proof that △stu ≅ △uvs.

statement
1 uv ≅ st
2 tu ≅ sv
3 su ≅ su
4
reason
given
given
reflexive property of congruence

Explanation:

Step1: Recall SSS Congruence Criterion

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the sides of the triangles

In \(\triangle STU\) and \(\triangle UVS\), we have \(\overline{UV}\cong\overline{ST}\) (given), \(\overline{TU}\cong\overline{SV}\) (given), and \(\overline{SU}\cong\overline{SU}\) (Reflexive Property of Congruence).

Step3: Apply SSS Congruence

By the Side - Side - Side (SSS) Congruence Criterion, \(\triangle STU\cong\triangle UVS\).

Answer:

\(\triangle STU\cong\triangle UVS\) (by SSS Congruence Criterion)