If \(\triangle ABC \sim \triangle PQR\) and AB : PQ = 2 : 3, then fill in the blanks.
\(\dfrac{A(\triangle ABC)}{A(\triangle PQR)} = \dfrac{AB^2}{\square} = \dfrac{2^2}{3^2} = \dfrac{\square}{\square}\)
Answer: \(\dfrac{A(\triangle ABC)}{A(\triangle PQR)} = \dfrac{AB^2}{PQ^2} = \dfrac{2^2}{3^2} = \dfrac{4}{9}\)
By the theorem of areas of similar triangles, the ratio of the areas of two similar triangles equals the ratio of the squares of their corresponding sides.
Since AB and PQ are corresponding sides,
\[\frac{A(\triangle ABC)}{A(\triangle PQR)} = \frac{AB^2}{PQ^2} = \frac{4}{9}\]Blanks: \(PQ^2\), 4, 9.
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