Question

rt ⊥ uw. complete the proof that ∠wvx ≅ ∠qsr.
statement\treason

1. rt ⊥ uw\tgiven
2. ∠wvx ≅ ∠tsv
3. ∠tsv ≅ ∠qsr
4. ∠wvx ≅ ∠qsr

Explanation:

Step1: Given parallel lines

Since $\overleftrightarrow{RT}\parallel\overleftrightarrow{UW}$, when two parallel lines are cut by a trans - versal, corresponding angles are congruent. $\angle WVX$ and $\angle TSV$ are corresponding angles, so $\angle WVX\cong\angle TSV$.

Step2: Vertical angles are congruent

$\angle TSV$ and $\angle QSR$ are vertical angles. By the vertical - angles theorem, vertical angles are congruent, so $\angle TSV\cong\angle QSR$.

Step3: Transitive property of congruence

Since $\angle WVX\cong\angle TSV$ and $\angle TSV\cong\angle QSR$, by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), we have $\angle WVX\cong\angle QSR$.

Answer:

1. Corresponding angles postulate
2. Vertical angles theorem
3. Transitive property of congruence