Question

complete the proof that ( overleftrightarrow{wy} parallel overleftrightarrow{tv} ).

1 ( overleftrightarrow{tv} parallel overleftrightarrow{hj} ) given
2 ( overleftrightarrow{wy} parallel overleftrightarrow{hj} ) given
3 ( angle sut cong angle his )
4 ( angle his cong angle sxw ) corresponding angles theorem
5 ( angle sut cong angle sxw )
6 ( overleftrightarrow{wy} parallel overleftrightarrow{tv} )

Explanation:

Step1: Identify the reason for \(\angle{SUT}\cong\angle{HIS}\)

Since \(\overleftrightarrow{TV}\parallel\overleftrightarrow{HJ}\), by the Corresponding Angles Theorem, \(\angle{SUT}\cong\angle{HIS}\).

Step2: Identify the reason for \(\angle{SUT}\cong\angle{SXW}\)

By the Transitive Property of Congruence, if \(\angle{SUT}\cong\angle{HIS}\) (from Step 1) and \(\angle{HIS}\cong\angle{SXW}\) (given as Corresponding Angles Theorem for \(\overleftrightarrow{WY}\parallel\overleftrightarrow{HJ}\)), then \(\angle{SUT}\cong\angle{SXW}\).

Step3: Identify the reason for \(\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}\)

By the Converse of the Corresponding Angles Theorem, if \(\angle{SUT}\cong\angle{SXW}\), then \(\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}\).

Answer:

1. Corresponding Angles Theorem; 5. Transitive Property of Congruence; 6. Converse of the Corresponding Angles Theorem.