Question

qs || eg and eg || tv. complete the proof that ∠puv ≅ ∠qrw.

statement
1 qs || eg
2 eg || tv
3 ∠puv ≅ ∠gfp
4 ∠gfp ≅ ∠qrw
5 ∠puv ≅ ∠qrw

reason
given
given
corresponding angles theorem

transitive property of congruence

Explanation:

Step1: Identify the relationship between lines and angles

Since \(\overleftrightarrow{EG}\parallel\overleftrightarrow{TV}\), and \(\angle GFP\) and \(\angle QRW\) are corresponding angles.

Step2: Apply the Corresponding Angles Theorem

By the Corresponding Angles Theorem, if two parallel lines are cut by a transversal, then corresponding angles are congruent. Here, \(\overleftrightarrow{EG}\) and \(\overleftrightarrow{TV}\) are parallel and cut by the transversal (the line containing \(GF\) and \(QR\)), so \(\angle GFP\cong\angle QRW\).

Answer:

Corresponding Angles Theorem