Question

vx || fh and su || fh. complete the proof that ∠rtu ≅ ∠vwy.

statement reason

1. vx || fh given
2. su || fh given
3. ∠vwy ≅ ∠fgy corresponding angles theorem
4. ∠fgy ≅ ∠rtu
5. ∠rtu ≅ ∠vwy alternate exterior angles theorem alternate interior angles theorem converse of alternate exterior angles theorem converse of alternate interior angles theorem converse of corresponding angles theorem

Explanation:

Step1: Identify parallel - lines

We are given that $\overleftrightarrow{VX}\parallel\overleftrightarrow{FH}$ and $\overleftrightarrow{SU}\parallel\overleftrightarrow{FH}$.

Step2: Apply corresponding - angles theorem

Since $\overleftrightarrow{VX}\parallel\overleftrightarrow{FH}$, by the Corresponding Angles Theorem, $\angle VWY\cong\angle FGY$.

Step3: Apply corresponding - angles theorem again

Since $\overleftrightarrow{SU}\parallel\overleftrightarrow{FH}$, $\angle FGY$ and $\angle RTU$ are corresponding angles. So, by the Corresponding Angles Theorem, $\angle FGY\cong\angle RTU$.

Step4: Use transitive property

If $\angle VWY\cong\angle FGY$ and $\angle FGY\cong\angle RTU$, then by the transitive property of congruence, $\angle RTU\cong\angle VWY$.

Answer:

Corresponding Angles Theorem