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 Similar Figures Proportion

For similar polygons, corresponding sides are proportional. So we need to match each side of the first figure (let's assume a quadrilateral \(ABCD\)) to the corresponding side of the second quadrilateral (say \(WXYZ\)). The order of the vertices matters, so \(AB\) corresponds to \(WX\), \(BC\) corresponds to \(XY\), \(CD\) corresponds to \(YZ\), and \(AD\) corresponds to \(WZ\).

Step2: Check Each Option

• Option A: \(\frac{BC}{WX}=\frac{CD}{XY}=\frac{AD}{YZ}=\frac{AB}{WZ}\) – Incorrect, as \(BC\) should correspond to \(XY\), not \(WX\).
• Option B: \(\frac{CD}{WX}=\frac{AD}{XY}=\frac{AB}{YZ}=\frac{BC}{WZ}\) – Incorrect, mismatched correspondences.
• Option C: \(\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}\) – Correct, as each side corresponds properly.
• Option D: \(\frac{AD}{WX}=\frac{AB}{XY}=\frac{BC}{YZ}=\frac{CD}{WZ}\) – Incorrect, mismatched correspondences.

Answer:

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