Question

eg || vx and eg || su. complete the proof that ∠uty ≅ ∠rwy.
statement reason
1 eg || vx given
2 eg || su given
3 ∠rwy ≅ ∠efr corresponding angles theorem
4 ∠efr ≅ ∠uty alternate interior angles theorem
5 ∠uty ≅ ∠rwy reflexive property of congruence reflexive property of equality substitution transitive property of congruence transitive property of equality

Explanation:

Step1: Identify given parallel - lines

Given $\overleftrightarrow{EG}\parallel\overleftrightarrow{VX}$ and $\overleftrightarrow{EG}\parallel\overleftrightarrow{SU}$.

Step2: Use corresponding - angles theorem

Since $\overleftrightarrow{EG}\parallel\overleftrightarrow{VX}$, by the corresponding - angles theorem, $\angle RWV\cong\angle EFR$.

Step3: Use alternate - interior angles theorem

Since $\overleftrightarrow{EG}\parallel\overleftrightarrow{SU}$, by the alternate - interior angles theorem, $\angle EFR\cong\angle UTY$.

Step4: Use transitive property of congruence

If $\angle RWV\cong\angle EFR$ and $\angle EFR\cong\angle UTY$, then by the transitive property of congruence, $\angle UTY\cong\angle RWV$.

Answer:

The reason for step 5 is Transitive Property of Congruence.