Question

complete the proof that ( \triangle stv cong \triangle ruv ).

Explanation:

Step1: Recall the Side - Angle - Side (SAS) Congruence Theorem

Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Step2: Identify the corresponding parts

In \(\triangle STV\) and \(\triangle RUV\):

• We have \(\overline{UV}\cong\overline{TV}\) (given)
• \(\overline{SV}\cong\overline{RV}\) (given)
• \(\angle RVU\cong\angle SVT\) (Vertical Angle Theorem)

The two sides \(\overline{UV}\) and \(\overline{SV}\) (in \(\triangle RUV\)) and \(\overline{TV}\) and \(\overline{SV}\) (in \(\triangle STV\)) along with the included angles \(\angle RVU\) and \(\angle SVT\) satisfy the SAS congruence criterion.

Answer:

Side - Angle - Side (SAS) Congruence Theorem.