Question

complete the proof that (overrightarrow{rt}paralleloverrightarrow{uw}). statement reason 1 (angle qstcongangle uvx) given 2 (angle qstcongangle rsv) vertical angle theorem 3 4

Explanation:

Step1: Transitive property of congruence

Since $\angle QST\cong\angle UVX$ (given) and $\angle QST\cong\angle RSV$ (vertical - angle theorem), by the transitive property of congruence, $\angle RSV\cong\angle UVX$.
Statement 3: $\angle RSV\cong\angle UVX$; Reason: Transitive property of congruence

Step2: Corresponding - angles postulate

If two lines are cut by a transversal such that a pair of corresponding angles are congruent, then the two lines are parallel. $\angle RSV$ and $\angle UVX$ are corresponding angles.
Statement 4: $\overrightarrow{RT}\parallel\overrightarrow{UW}$; Reason: Corresponding - angles postulate

Answer:

Statement 3: $\angle RSV\cong\angle UVX$; Reason: Transitive property of congruence
Statement 4: $\overrightarrow{RT}\parallel\overrightarrow{UW}$; Reason: Corresponding - angles postulate