Question

determine if triangle stu and triangle vwx 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 - equality

One pair of angles are equal, $\angle S=\angle V = 24^{\circ}$.

Step2: Check side - ratio

Calculate the ratio of corresponding sides. $\frac{SV}{ST}=\frac{56}{14} = 4$ and $\frac{VW}{SU}=\frac{60}{15}=4$.

Step3: Apply similarity criterion

Since one pair of angles are equal and the sides including these angles are in proportion, by the Side - Angle - Side (SAS) similarity criterion, the triangles are similar.

Answer:

The triangles $STU$ and $VWX$ are similar by the SAS (Side - Angle - Side) similarity criterion.