Question

fh || rt and fh || uw. complete the proof that ∠qsr ≅ ∠wvx.
1 fh || rt given
2 fh || uw given
3 ∠wvx ≅ ∠hgx corresponding angles theorem
4 ∠hgx ≅ ∠qsr
5 ∠qsr ≅ ∠wvx transitive property of congruence

Explanation:

Step1: Recall the Corresponding Angles Theorem

Since \(\overleftrightarrow{FH}\parallel\overleftrightarrow{RT}\), when a transversal \( \overleftrightarrow{QX}\) intersects them, \(\angle HGX\) and \(\angle QSR\) are corresponding angles.

Step2: Apply the Corresponding Angles Theorem

By the Corresponding Angles Theorem, if two parallel lines are cut by a transversal, then the corresponding angles are congruent. So, \(\angle HGX\cong\angle QSR\) because \(\overleftrightarrow{FH}\parallel\overleftrightarrow{RT}\) and \( \overleftrightarrow{QX}\) is the transversal.

Answer:

Corresponding Angles Theorem