Question

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

Explanation:

Step1: Identify vertical angles

$\angle QSR = \angle US T$ (vertical angles are congruent)

Step2: Find $\angle R$ in $\triangle QRS$

Sum of angles in a triangle is $180^\circ$.
$\angle R = 180^\circ - 55^\circ - \angle QSR$

Step3: Find $\angle U$ in $\triangle UST$

Sum of angles in a triangle is $180^\circ$.
$\angle U = 180^\circ - 65^\circ - \angle US T$
Since $\angle QSR = \angle US T$, $\angle R
eq \angle U$, and $\angle Q
eq \angle T$. No two pairs of corresponding angles are congruent, and the sides with the marked congruence are not in proportion for SAS similarity (we only know one pair of vertical angles and non-corresponding congruent sides).

Answer:

$\triangle QRS$ is not similar to $\triangle UST$.