Question

complete the proof that ∠uxy ≅ ∠tux.
statement reason

1. wy || tv given
2. ∠uxy ≅ ∠suv corresponding angles theorem
3. ∠suv ≅ ∠tux vertical angle theorem
4. ∠uxy ≅ ∠tux properties of addition, subtraction, multiplication, and division, reflexive property of congruence, reflexive property of equality, substitution, transitive property of congruence, transitive property of equality

Explanation:

Step1: Identify given parallel lines

Given $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$.

Step2: Apply corresponding - angles theorem

Since $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$, by the Corresponding Angles Theorem, $\angle UXY\cong\angle SUV$.

Step3: Apply vertical - angles theorem

$\angle SUV$ and $\angle TUX$ are vertical angles. By the Vertical Angle Theorem, $\angle SUV\cong\angle TUX$.

Step4: Use transitive property of congruence

We know that if $\angle UXY\cong\angle SUV$ and $\angle SUV\cong\angle TUX$, then by the Transitive Property of Congruence, $\angle UXY\cong\angle TUX$.

Answer:

Transitive Property of Congruence