Question

complete the proof that ∠svw≅∠tuw. statement reason 1 ∠utw≅∠s given 2 (overleftrightarrow{tu}paralleloverleftrightarrow{sv}) given 3 ∠s≅∠tuw alternate interior angles theorem 4 ∠utw≅∠svw alternate interior angles theorem 5 ∠s≅∠svw transitive property of congruence 6 ∠svw≅∠tuw reflexive property of congruence reflexive property of equality substitution transitive property of congruence transitive property of equality

Explanation:

Step1: Recall given congruences

We know from statements 1 and 3 that $\angle UTW\cong\angle S$ and $\angle S\cong\angle TUW$.

Step2: Apply transitive property

The transitive property of congruence states that if $a\cong b$ and $b\cong c$, then $a\cong c$. Here, $a = \angle UTW$, $b=\angle S$ and $c = \angle TUW$. Also, from statement 4 $\angle UTW\cong\angle SVW$. Combining with $\angle S\cong\angle TUW$ and using transitive - like logic for the congruence of angles related to $\angle S$, we can show $\angle SVW\cong\angle TUW$.

Answer:

Transitive Property of Congruence