Question

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 the ratio of corresponding sides

For $\triangle STU$ and $\triangle VWX$, if they are similar, the ratios of corresponding - sides should be equal. Let's assume $ST$ corresponds to $VW$, $SU$ corresponds to $VX$, and $TU$ corresponds to $WX$. Calculate the ratios of the sides: $\frac{ST}{VW}=\frac{15}{60}=\frac{1}{4}$, $\frac{SU}{VX}=\frac{14}{56}=\frac{1}{4}$.

Step2: Check the included - angle

The included angle between $ST$ and $SU$ in $\triangle STU$ is $\angle S = 74^{\circ}$, and the included angle between $VW$ and $VX$ in $\triangle VWX$ is $\angle V=74^{\circ}$. Since the ratios of two pairs of corresponding sides are equal ($\frac{ST}{VW}=\frac{SU}{VX}=\frac{1}{4}$) and the included angles are equal ($\angle S=\angle V = 74^{\circ}$), by the Side - Angle - Side (SAS) similarity criterion, the two triangles are similar.

Answer:

The triangles are similar. We know this because the ratios of two pairs of corresponding sides are equal ($\frac{ST}{VW}=\frac{SU}{VX}=\frac{1}{4}$) and the included angles between those sides are equal ($\angle S=\angle V = 74^{\circ}$).