Question

consider the two triangles. how can the triangles be proven similar by the sss similarity theorem? show that the ratios \\( \frac { u v } { x y } \\), \\( \frac { w u } { z x } \\), and \\( \frac { w v } { z y } \\) are equivalent. show that the ratios \\( \frac { u v } { z y } \\), \\( \frac { w u } { z x } \\), and \\( \frac { w v } { x y } \\) are equivalent. show that the ratios \\( \frac { u v } { x y } \\) and \\( \frac { w v } { z y } \\) are equivalent, and \\( \angle v \cong \angle y \\). show that the ratios \\( \frac { u v } { z y } \\) and \\( \frac { w u } { z x } \\) are equivalent, and \\( \angle u \cong \angle z \\).

Explanation:

Step1: Recall SSS similarity theorem

SSS similarity theorem states that if the ratios of the corresponding sides of two triangles are equal, then the triangles are similar.

Step2: Identify corresponding sides

In \(\triangle UVW\) and \(\triangle ZYX\), \(UV = 50\), \(WU=40\), \(WV = 60\), \(ZY = 40\), \(ZX = 32\), \(XY=48\).
We need to check the ratios \(\frac{UV}{ZY}=\frac{50}{40}=\frac{5}{4}\), \(\frac{WU}{ZX}=\frac{40}{32}=\frac{5}{4}\), \(\frac{WV}{XY}=\frac{60}{48}=\frac{5}{4}\)

Answer:

Show that the ratios \(\frac{UV}{ZY},\frac{WU}{ZX},\) and \(\frac{WV}{XY}\) are equivalent.