In the following figure $, / / / m / / n .$ If $O C = O D = 5 c m, O A = 8 c m$ and $O E = 10 c m,$ find $O F$ .

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Solution

Given: $l ∥ m ∥ n$ ,

In $△ O A C$ and $△ O B D$ ,
$∠ A O C = ∠ D O B$ (Vertically opposite angles)
$∠ O C A = ∠ O D B$ (Alternate angles of parallel lines)
$∠ O A C = ∠ O B D$ (Alternate angles of parallel lines)
Thus, $△ O A C \sim △ O B D$ (AAA rule)
$\frac{O A}{O B} = \frac{O C}{O D}$
$\frac{8}{O B} = \frac{5}{5}$
$O B = 8$ cm

Similarly, $△ O E C \sim △ O F D$ (AAA rule)
$\frac{O E}{O F} = \frac{O C}{O D}$
$\frac{10}{O F} = \frac{5}{5}$
$O F = 10$ cm

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