Question

determine if triangle pqr and triangle stu are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Check angle - angle similarity

We have $\angle Q = 50^{\circ}$ and $\angle U=50^{\circ}$, and $\angle T = 50^{\circ}$. In $\triangle PQR$, if $\angle Q = 50^{\circ}$, and in $\triangle STU$, $\angle U = 50^{\circ}$ and $\angle T=50^{\circ}$. Since two angles of $\triangle PQR$ are equal to two angles of $\triangle STU$ (we can assume the third - angle will also be equal as the sum of angles in a triangle is $180^{\circ}$).

Step2: State the similarity criterion

By the AA (angle - angle) similarity criterion, if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.

Answer:

The triangles $PQR$ and $STU$ are similar by the AA (angle - angle) similarity criterion.