Question

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complete the proof that ∠suv≅∠wxz.
statement reason
1 wy || tv given
2 ∠wxz≅∠tux corresponding angles theorem
3 ∠tux≅∠suv vertical angle theorem
4 ∠suv≅∠wxz 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: Recall given equal - angle relationships

We are given that $\angle WXZ\cong\angle TUX$ (by the Corresponding Angles Theorem) and $\angle TUX\cong\angle SUV$ (by the Vertical Angle Theorem).

Step2: Apply the Transitive Property of Congruence

The Transitive Property of Congruence states that if $\angle A\cong\angle B$ and $\angle B\cong\angle C$, then $\angle A\cong\angle C$. Here, $A = \angle SUV$, $B=\angle TUX$, and $C = \angle WXZ$. So, since $\angle WXZ\cong\angle TUX$ and $\angle TUX\cong\angle SUV$, we can conclude that $\angle SUV\cong\angle WXZ$.

Answer:

Transitive Property of Congruence