Question

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

the triangles ​ similar.

Explanation:

Step1: Identify side lengths of each triangle

For $\triangle UVW$: $UV = 14$, $UW = 14$, $VW = 18$.
For $\triangle XYZ$: $XZ = 56$, $XY = 56$, $YZ = 72$.

Step2: Check ratios of corresponding sides

• Ratio of $UV$ to $XZ$: $\frac{UV}{XZ}=\frac{14}{56}=\frac{1}{4}$
• Ratio of $UW$ to $XY$: $\frac{UW}{XY}=\frac{14}{56}=\frac{1}{4}$
• Ratio of $VW$ to $YZ$: $\frac{VW}{YZ}=\frac{18}{72}=\frac{1}{4}$

All corresponding sides are in proportion ($\frac{1}{4}$), so by the SSS (Side - Side - Side) similarity criterion, the triangles are similar.

Answer:

The triangles are similar. We know this because the ratios of their corresponding sides are equal ($\frac{14}{56}=\frac{14}{56}=\frac{18}{72}=\frac{1}{4}$), satisfying the SSS similarity condition.