Question

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

Explanation:

Step1: Recall SSS similarity rule

SSS similarity requires all three corresponding side ratios to be equal.

Step2: Identify corresponding sides

Triangle UVW has sides UV=50, WU=40, WV=60. Triangle XZY has sides ZX=32, ZY=48, XY=40. Corresponding sides: UV↔ZY, WU↔ZX, WV↔XY.

Step3: Check ratio equivalence

Ratios: $\frac{UV}{ZY}=\frac{50}{48}=\frac{25}{24}$, $\frac{WU}{ZX}=\frac{40}{32}=\frac{5}{4}$? No, wait—correction: Correct correspondence should match side lengths. UV=50, XY=40; WU=40, ZX=32; WV=60, ZY=48. Ratios: $\frac{UV}{XY}=\frac{50}{40}=\frac{5}{4}$, $\frac{WU}{ZX}=\frac{40}{32}=\frac{5}{4}$, $\frac{WV}{ZY}=\frac{60}{48}=\frac{5}{4}$. These are equivalent.

Step4: Match with options

The first option says show $\frac{UV}{XY}$, $\frac{WU}{ZX}$, $\frac{WV}{ZY}$ are equivalent—this fits.

Answer:

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