Question

complete the proof that m∠rsv + m∠svu = 180°. statement reason 1 uw || rt given 2 ∠svu ≅ ∠qsr 3 m∠qsr + m∠rsv = 180° angles forming a linear pair sum to 180° converse of corresponding angles theorem 4 m∠rsv + m∠svu = 180° corresponding angles theorem definition of congruence definition of supplementary angles

Explanation:

Step1: Identify given parallel lines

Given $\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}$.

Step2: Use corresponding - angles theorem

Since $\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}$, by the Corresponding Angles Theorem, $\angle SVU\cong\angle QSR$. The reason for $\angle SVU\cong\angle QSR$ is the Corresponding Angles Theorem.

Step3: Recall linear - pair property

We know that $\angle QSR$ and $\angle RSV$ form a linear pair. By the property that angles forming a linear pair sum to $180^{\circ}$, we have $m\angle QSR + m\angle RSV=180^{\circ}$.

Step4: Substitute equal - measure angles

Since $\angle SVU\cong\angle QSR$, by the Definition of congruence (if two angles are congruent, their measures are equal), we can substitute $m\angle QSR$ with $m\angle SVU$ in the equation $m\angle QSR + m\angle RSV = 180^{\circ}$. So, $m\angle RSV + m\angle SVU=180^{\circ}$.

Answer:

The reason for $\angle SVU\cong\angle QSR$ is the Corresponding Angles Theorem.