Questions: The diagram below includes similar quadrilaterals. Find the length of AB.

Solution Steps

Since the quadrilaterals are similar, the corresponding sides are proportional. Identify the corresponding sides:

• $AB$ corresponds to $EF$
• $BC$ corresponds to $FG$
• $CD$ corresponds to $GH$
• $DA$ corresponds to $HE$

Using the corresponding sides, set up the proportion: $$\frac{AB}{EF} = \frac{BC}{FG} = \frac{CD}{GH} = \frac{DA}{HE}$$

Substitute the known values into the proportion: $$\frac{AB}{8} = \frac{7.5}{4} = \frac{6}{6} = \frac{9}{6}$$

Use the proportion involving $AB$ and $EF$: $$\frac{AB}{8} = \frac{9}{6}$$ $$AB = 8 \times \frac{9}{6}$$ $$AB = 8 \times 1.5$$ $$AB = 12$$

Final Answer