Question

complete the proof that ∠tuz≅∠sxy.
statement\treason
1\ttv || gi
2\twy || gi
3\t∠sxy≅∠ihs
4\t∠ihs≅∠tuz
5\t∠tuz≅∠sxy

Explanation:

Step1: Given information

Given that $\overrightarrow{TV}\parallel\overrightarrow{GI}$ and $\overrightarrow{WY}\parallel\overrightarrow{GI}$ (usually given in the problem - context or diagram - related information).

Step2: Corresponding - angle property

Since $\overrightarrow{WY}\parallel\overrightarrow{GI}$, $\angle SXY\cong\angle IHS$ because corresponding angles formed by parallel lines and a transversal are congruent.

Step3: Vertical - angle property

$\angle IHS\cong\angle TUZ$ because vertical angles are congruent.

Step4: Transitive property of congruence

Since $\angle SXY\cong\angle IHS$ and $\angle IHS\cong\angle TUZ$, by the transitive property of congruence, $\angle TUZ\cong\angle SXY$.

Answer:

1. Given
2. Given
3. Corresponding angles of parallel lines are congruent
4. Vertical angles are congruent
5. Transitive property of congruence