Question

f 7.2 g 3.9 3.9 i 7.2 h ghif ~ tqrs 3.9/6 = 3.9/6 = 7.2/12 t 6 q 12 12 s 6

Explanation:

Step1: Check Proportions

For similar polygons \( GHIF \sim TQRS \), corresponding sides should be proportional. Let's check the ratios:

• Ratio of \( FI \) (3.9) to \( TQ \) (6): \( \frac{3.9}{6}=0.65 \)
• Ratio of \( GH \) (3.9) to \( RS \) (6)? Wait, no, correct correspondence: \( FI \) corresponds to \( TQ \), \( FG \) (7.2) corresponds to \( TS \) (12), \( IH \) (7.2) corresponds to \( SQ \)? Wait, re - identify sides. In \( GHIF \), sides: \( FI = 3.9 \), \( FG=7.2 \), \( GH = 3.9 \), \( HI = 7.2 \). In \( TQRS \), sides: \( TQ = 6 \), \( TS = 12 \), \( SR = 6 \), \( RQ = 12 \).

So correct ratios: \( \frac{FI}{TQ}=\frac{3.9}{6} = 0.65 \), \( \frac{FG}{TS}=\frac{7.2}{12}=0.6 \). These ratios are not equal, so the given proportion \( \frac{3.9}{6}=\frac{3.9}{6}=\frac{7.2}{12} \) is wrong because \( \frac{3.9}{6}=0.65 \) and \( \frac{7.2}{12} = 0.6 \), and \( 0.65
eq0.6 \).

Step2: Find Correct Proportion

The correct ratio should be based on corresponding sides. Let's find the scale factor. Let's take \( FI = 3.9 \) and its corresponding side in \( TQRS \). Wait, maybe the correspondence is wrong. Let's re - establish similarity. For parallelograms (both figures are parallelograms as opposite sides are equal), the similarity ratio should be between corresponding sides. Let's check \( FI = 3.9 \) and \( RQ = 12 \)? No, better to see the lengths. In \( GHIF \), side lengths: 3.9, 7.2, 3.9, 7.2. In \( TQRS \), side lengths: 6, 12, 6, 12. The ratio of small side to small side: \( \frac{3.9}{6}=0.65 \), large side to large side: \( \frac{7.2}{12}=0.6 \). These are not equal, so the figures are not similar with the given proportion. But if we correct the correspondence, maybe the small sides (3.9) correspond to 6? No, actually, the error is in the proportion calculation because \( \frac{3.9}{6}=0.65 \) and \( \frac{7.2}{12}=0.6 \), so \( \frac{3.9}{6}
eq\frac{7.2}{12} \).

Answer:

The given proportion \( \frac{3.9}{6}=\frac{3.9}{6}=\frac{7.2}{12} \) is incorrect because \( \frac{3.9}{6} = 0.65 \) and \( \frac{7.2}{12}=0.6 \), and \( 0.65
eq0.6 \). The correct proportion should have equal ratios for corresponding sides.