consider the two triangles. how can the triangles be proven similar by the sas similarity theorem? show that…

consider the two triangles. how can the triangles be proven similar by the sas similarity theorem? show that the ratios $\frac{xy}{vu}$ and $\frac{yz}{vw}$ are equivalent, and $angle ucongangle x$. show that the ratios $\frac{uv}{xy}$ and $\frac{wv}{zy}$ are equivalent, and $angle vcongangle y$. show that the ratios $\frac{uw}{zx}$ and $\frac{xy}{wv}$ are equivalent, and $angle wcongangle x$. show that the ratios $\frac{xz}{wu}$ and $\frac{zy}{wv}$ are equivalent, and $angle ucongangle z$.

consider the two triangles. how can the triangles be proven similar by the sas similarity theorem? show that the ratios $\frac{xy}{vu}$ and $\frac{yz}{vw}$ are equivalent, and $angle ucongangle x$. show that the ratios $\frac{uv}{xy}$ and $\frac{wv}{zy}$ are equivalent, and $angle vcongangle y$. show that the ratios $\frac{uw}{zx}$ and $\frac{xy}{wv}$ are equivalent, and $angle wcongangle x$. show that the ratios $\frac{xz}{wu}$ and $\frac{zy}{wv}$ are equivalent, and $angle ucongangle z$.

Answer

Answer:

Show that the ratios $\frac{UV}{XY}$ and $\frac{WV}{ZY}$ are equivalent, and $\angle V\cong\angle Y$.

Explanation:

Step1: Recall SAS similarity theorem

The SAS (Side - Angle - Side) similarity theorem states that if the ratios of two pairs of corresponding sides of two triangles are equal and the included angles are congruent, then the two triangles are similar.

Step2: Identify corresponding sides and angle

In $\triangle UVW$ and $\triangle XYZ$, we need to find the pairs of corresponding sides and the included congruent angle. The sides adjacent to $\angle V$ in $\triangle UVW$ are $UV$ and $WV$, and the sides adjacent to $\angle Y$ in $\triangle XYZ$ are $XY$ and $ZY$. We need to show $\frac{UV}{XY}=\frac{WV}{ZY}$ and $\angle V\cong\angle Y$ for SAS similarity.