Question

figure i and figure ii are similar figures. the side lengths are given in millimeters.
which proportion must be true?
a $\frac{8}{5}=\frac{8}{a}$
b $\frac{b}{6.4}=\frac{5}{3.2}$
c $\frac{2}{3.2}=\frac{8}{a}$
d $\frac{b}{2}=\frac{3.2}{6.4}$

Explanation:

Step1: Recall the property of similar figures

For similar figures, the ratios of corresponding side lengths are equal.

Step2: Analyze each option

• Option A:

The sides \(8\) (from Figure I) and \(8\) (from Figure II) are not corresponding sides. So, \(\frac{8}{5}
eq\frac{8}{a}\)

• Option B:

The sides \(b\) (from Figure I) and \(5\) (from Figure I) are not in the same ratio relationship as \(\frac{b}{6.4}\) and \(\frac{5}{3.2}\). Because \(b\) corresponds to \(6.4\) and \(5\) corresponds to \(8\)

• Option C:

The side \(2\) (from Figure I) corresponds to \(3.2\) (from Figure II), and \(8\) (from Figure I) corresponds to \(a\) (from Figure II). So, \(\frac{2}{3.2}=\frac{8}{a}\) (by the property of similar - figure side - length ratios)

• Option D:

The ratio \(\frac{b}{2}=\frac{3.2}{6.4}\) is incorrect. Since \(b\) corresponds to \(6.4\) and \(2\) corresponds to \(3.2\), the correct ratio should be \(\frac{b}{6.4}=\frac{2}{3.2}\)

Answer:

C. \(\frac{2}{3.2}=\frac{8}{a}\)