Question

rt || uw. complete the proof that ∠qsr ≅ ∠wvx.
statement

1. rt || uw
2. ∠wvx ≅ ∠tsv
3. ∠tsv ≅ ∠qsr
4. ∠qsr ≅ ∠wvx

reason
given

Explanation:

Step1: Identify angle - pair relationship for step 2

Corresponding angles postulate.
Since $\overrightarrow{RT}\parallel\overrightarrow{UW}$, $\angle WVX$ and $\angle TSV$ are corresponding angles, so $\angle WVX\cong\angle TSV$.

Step2: Identify angle - pair relationship for step 3

Vertical angles are congruent.
$\angle TSV$ and $\angle QSR$ are vertical angles, so $\angle TSV\cong\angle QSR$.

Step3: Use transitive property for step 4

Transitive property of congruence.
Since $\angle WVX\cong\angle TSV$ and $\angle TSV\cong\angle QSR$, then $\angle QSR\cong\angle WVX$ by the transitive property of congruence.

Answer:

1. Corresponding angles postulate; 3. Vertical angles are congruent; 4. Transitive property of congruence.