Question

ru || sv. complete the proof that tv ≅ su.

statement
1 ∠u ≅ ∠v
2 ru || sv
3 ru ≅ sv
4 ∠sru ≅ ∠tsv
5

reason
given
given
given
corresponding angles theorem

Explanation:

Step1: Use ASA (Angle - Side - Angle) Congruence

We know that in triangles \( \triangle SRU\) and \( \triangle STV\):

• \( \angle U\cong\angle V\) (Given)
• \( \overline{RU}\cong\overline{SV}\) (Given)
• \( \angle SRU\cong\angle TSV\) (Corresponding Angles Theorem)

By the ASA (Angle - Side - Angle) congruence criterion, \( \triangle SRU\cong\triangle STV\).

Step2: Use CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Since \( \triangle SRU\cong\triangle STV\), then their corresponding sides \( \overline{TV}\) and \( \overline{SU}\) are congruent.

Answer:

\(\triangle SRU\cong\triangle STV\) (by ASA), so \(\overline{TV}\cong\overline{SU}\) (by CPCTC)