In the figure given below, $∠ P Q R = ∠ P R S$ . Prove that triangles $P Q R$ and $P R S$ are similar. If $P R = 8 c m, P S = 4 c m$ , calculate $P Q$ .

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Solution

From the figure,
$∠ P = ∠ P$ (common angle for both triangles)
$∠ P Q R = ∠ P R S$ [from the question]
So, $△ P Q R \sim △ P R S$
Then, $P Q / P R = P R / P S = Q R / S R$
Consider $P Q / P R = P R / P S$
$P Q / 8 = 8 / 4$
$P Q = (8 \times 8) / 4$
$P Q = 64 / 4$
$P Q = 16 c m$ .

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