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 paired sides/included angle

For $\triangle UVW$: sides adjacent to $49^\circ$ are $VW=16$, $UW=22$; included angle $\angle W=49^\circ$.
For $\triangle XYZ$: match sides to check ratios:

Step2: Calculate side ratios

Ratio of $VW$ to $ZY$: $\frac{16}{80}=\frac{1}{5}$
Ratio of $UW$ to $XY$: $\frac{22}{110}=\frac{1}{5}$
Ratio of $UV$ to $XZ$: $\frac{28}{140}=\frac{1}{5}$

Step3: Verify SAS similarity

The included angle for $\triangle XYZ$ would be between sides $ZY$ and $XY$ (matching the included angle position in $\triangle UVW$). Since all corresponding side ratios are equal, and the included angle condition is satisfied for SAS (or all sides proportional for SSS).

Answer:

The triangles are similar, by the SSS (Side-Side-Side) Similarity Criterion (or SAS, since the included angle is between the paired sides with equal ratios), as all corresponding side lengths are in the same ratio of $\frac{1}{5}$.