Question

qs and tv are parallel lines. select all the pairs of alternate interior angles. ∠sru and ∠tur ∠sru and ∠qrp ∠sru and ∠vur ∠qru and ∠vur

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each pair

• For \(\angle SRU\) and \(\angle TUR\):

Since \(\overleftrightarrow{QS}\parallel\overleftrightarrow{TV}\) and \(WP\) is the transversal. \(\angle SRU\) and \(\angle TUR\) lie between \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\) and on opposite sides of \(WP\), so they are alternate - interior angles.

• For \(\angle SRU\) and \(\angle QRP\):

\(\angle QRP\) and \(\angle TUR\) are vertical angles (\(\angle QRP=\angle TUR\)). Since \(\angle SRU\) and \(\angle TUR\) are alternate - interior angles, and \(\angle QRP=\angle TUR\), but \(\angle SRU\) and \(\angle QRP\) do not satisfy the position relationship of alternate - interior angles (they are not between the two parallel lines in the correct sense for the definition).

• For \(\angle SRU\) and \(\angle VUR\):

\(\angle SRU\) and \(\angle VUR\) do not lie between the two parallel lines \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\) in the way required for alternate - interior angles.

• For \(\angle QRU\) and \(\angle VUR\):

Since \(\overleftrightarrow{QS}\parallel\overleftrightarrow{TV}\) and \(WP\) is the transversal. \(\angle QRU\) and \(\angle VUR\) lie between \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\) and on opposite sides of \(WP\), so they are alternate - interior angles.

Answer:

\(\angle SRU\) and \(\angle TUR\), \(\angle QRU\) and \(\angle VUR\)