Question

which proportion must be true?
a $\frac { s t } { e f } = \frac { w r } { c d }$
b $\frac { w v } { a b } = \frac { s t } { e f }$
c $\frac { r s } { a b } = \frac { t u } { c d }$
d $\frac { t u } { a b } = \frac { u v } { a f }$

Explanation:

Step1: Recall the property of similar polygons

For similar polygons, the ratios of corresponding sides are equal.

Step2: Analyze each option

• Option A: \(ST\) and \(EF\) are not corresponding sides, \(WR\) and \(CD\) are not corresponding sides. So \(\frac{ST}{EF}=\frac{WR}{CD}\) is not valid.
• Option B: \(WV\) and \(AB\) are corresponding sides, \(ST\) and \(EF\) are corresponding sides. So \(\frac{WV}{AB}=\frac{ST}{EF}\) is valid.
• Option C: \(RS\) and \(AB\) are not corresponding sides, \(TU\) and \(CD\) are not corresponding sides. So \(\frac{RS}{AB}=\frac{TU}{CD}\) is not valid.
• Option D: \(TU\) and \(AB\) are corresponding sides, \(UV\) and \(AF\) are not corresponding sides. So \(\frac{TU}{AB}=\frac{UV}{AF}\) is not valid.

Answer:

B. \(\frac{WV}{AB}=\frac{ST}{EF}\)