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 (Side - Side - Side) 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 \(\triangle ZYX\), \(UV = 50\), \(WU=40\), \(WV = 60\) and \(ZY = 48\), \(ZX = 32\), \(XY = 40\)

We need to check the ratios of corresponding sides.
For SSS similarity, we should match the sides of \(\triangle UVW\) with the sides of \(\triangle ZYX\) as follows:
\(\frac{UV}{ZY}=\frac{50}{40}=\frac{5}{4}\), \(\frac{WU}{ZX}=\frac{40}{32}=\frac{5}{4}\), \(\frac{WV}{XY}=\frac{60}{48}=\frac{5}{4}\)

Answer:

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