Question

select the proportion that relates the corresponding sides.
a) $\frac{bc}{wx}=\frac{cd}{xy}=\frac{ad}{yz}=\frac{ab}{wz}$
b) $\frac{cd}{wx}=\frac{ad}{xy}=\frac{ab}{yz}=\frac{bc}{wz}$
c) $\frac{ab}{wx}=\frac{bc}{xy}=\frac{cd}{yz}=\frac{ad}{wz}$
d) $\frac{ad}{wx}=\frac{ab}{xy}=\frac{bc}{yz}=\frac{cd}{wz}$

Explanation:

Step1: Recall side - proportion rule for similar polygons

In similar polygons, the ratios of corresponding sides are equal. If two polygons are similar, the order of the vertices matters when writing the proportion of corresponding sides.

Step2: Analyze the order of vertices

Assume the two polygons are similar. The correct proportion should have corresponding sides in the same relative position in the ratio. For example, if we consider the first - named side of one polygon, it should be compared to the first - named side of the other polygon in the ratio.
Let's assume the two polygons have vertices in a certain order. The correct proportion of corresponding sides should be such that the sides that correspond to each other are in the same position in the fraction. If we assume the first polygon has sides \(AB, BC, CD, DA\) and the second has sides \(WX, XY, YZ, WZ\) respectively, the correct proportion is \(\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}\)

Answer:

C. \(\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}\)