Question

which of the following best completes the proof showing that δwxz ~ δxyz? since xz ⊥ wy, angles wzx and xzy are both right angles and congruent. the proportion ____ shows the corresponding sides are proportional, so the triangles are similar by the sas similarity postulate.

1. $\frac{6}{12}=\frac{3}{6}$
2. $\frac{6}{3}=\frac{6}{12}$
3. $\frac{6}{6}=\frac{3}{12}$

Explanation:

Step1: Identify corresponding sides

For $\triangle WXZ$ and $\triangle XYZ$, the sides adjacent to the right - angles are considered. In $\triangle WXZ$, the sides are $WZ = 12$ and $XZ=6$. In $\triangle XYZ$, the sides are $XZ = 6$ and $ZY = 3$.

Step2: Set up proportion for SAS

The SAS (Side - Angle - Side) similarity postulate requires the ratio of the corresponding sides to be equal. The ratio of the sides should be $\frac{WZ}{XZ}=\frac{XZ}{ZY}$. Substituting the values, we get $\frac{12}{6}=\frac{6}{3}$, which is equivalent to $\frac{6}{3}=\frac{6}{12}$ when cross - multiplied.

Answer:

$\frac{6}{3}=\frac{6}{12}$