Question

1. figure i and figure ii are similar quadrilaterals.

which proportion must be true?
a. $\frac{3.2}{2} = \frac{8}{8}$
b. $\frac{a}{b} = \frac{8}{5}$
c. $\frac{b}{6.4} = \frac{8}{5}$
d. $\frac{2}{3.2} = \frac{b}{a}$

Explanation:

Step1: Match corresponding sides

For similar quadrilaterals, corresponding sides form equal ratios.
From Figure I and II:

• 2 mm (Figure I) ↔ 3.2 mm (Figure II)
• 8 mm (Figure I) ↔ \(a\) mm (Figure II)
• \(b\) mm (Figure I) ↔ 6.4 mm (Figure II)
• 5 mm (Figure I) ↔ 8 mm (Figure II)

Step2: Test each option

Option A: $\frac{3.2}{2} = \frac{a}{8}$ → $\frac{\text{Figure II side}}{\text{Figure I side}} = \frac{\text{Figure II side}}{\text{Figure I side}}$. This follows the similarity ratio.
Option B: $\frac{a}{b} = \frac{8}{5}$ → Mixes Figure II and I sides incorrectly in ratios.
Option C: $\frac{b}{6.4} = \frac{8}{5}$ → Incorrect corresponding side pairing.
Option D: $\frac{2}{3.2} = \frac{b}{a}$ → Incorrect corresponding side pairing.

Answer:

A. $\frac{3.2}{2} = \frac{a}{8}$