To determine if the triangles are congruent we are going to use the SAS theorem of similarity.
SAS stands for "side, angle, side" and means that we have two triangles where:
• the ratio between two sides is the same as the ratio between another two sides
,
• and we we also know the included angles are equal.
Notice that the ratio between sides QW and SW is the same as the ratio between RW and ZW:
[tex]\begin{gathered} \frac{15}{45}=\frac{14}{42} \\ \frac{1}{3}=\frac{1}{3} \end{gathered}[/tex]
hence the first condition of the theorem is fullfil.
We also notice that angle W is the same for triangle SZW and QRW, therefore the second condition for the theorem is alsso fullfilled.
Therefore we concldue that the triangles are similar.
