Question

complete the proof that ∠qst ≅ ∠uvx.
statement reason
1 rt || uw given
2 ∠uvx ≅ ∠rsv corresponding angles theorem
3 ∠rsv ≅ ∠qst vertical angle theorem
4 ∠qst ≅ ∠uvx 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: Identificar los ángulos congruentes dados

Tenemos $\angle UVX\cong\angle RSV$ (por el Teorema de Ángulos Correspondientes) y $\angle RSV\cong\angle QST$ (por el Teorema de Ángulos Verticales).

Step2: Aplicar la propiedad transitiva

Si $\angle UVX\cong\angle RSV$ y $\angle RSV\cong\angle QST$, entonces por la Propiedad Transitiva de la Congruencia, $\angle QST\cong\angle UVX$.

Answer:

Transitive Property of Congruence