Question

qs || tv. complete the proof that ( mangle prq + mangle tuw = 180^{circ} ).

Explanation:

Step1: Corresponding angles

Since \(\overleftrightarrow{QS}\parallel\overleftrightarrow{TV}\), by the Corresponding Angles Theorem, \(\angle TUW\cong\angle QRU\).

Step2: Linear pair

\(\angle PRQ\) and \(\angle QRU\) form a linear pair. By the Linear Pair Postulate, \(m\angle PRQ + m\angle QRU=180^{\circ}\).

Step3: Substitution

Since \(\angle TUW\cong\angle QRU\) (from Step 1), we can substitute \(m\angle QRU\) with \(m\angle TUW\) in the equation \(m\angle PRQ + m\angle QRU = 180^{\circ}\) (from Step 2). So \(m\angle PRQ + m\angle TUW=180^{\circ}\).

Answer:

1. Corresponding Angles Theorem; 3. Linear Pair Postulate; 4. Substitution Property of Equality.