Question

△qsu and △rst are shown below.
which statement is true?
△qsu is similar to △rst.
△qsu is not similar to △rst.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Identify Parallel Lines and Angles

From the diagram, \( QU \parallel RT \) (indicated by the red arrows, meaning they are parallel). So, \( \angle Q \cong \angle R \) and \( \angle U \cong \angle T \) (corresponding angles for parallel lines cut by transversals \( QS \) and \( US \)).

Step2: Apply AA Similarity Criterion

The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. In \( \triangle QSU \) and \( \triangle RST \), we have \( \angle Q \cong \angle R \) and \( \angle U \cong \angle T \). So, by AA similarity, \( \triangle QSU \sim \triangle RST \).

Answer:

\(\triangle QSU\) is similar to \(\triangle RST\).