In the given figure, $A B$ is a parallel to $D E .$ If $A C = 6 c m, C E = 15 c m$ and $D B = 28 c m,$ find $D C$

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Solution

In $△ A C B$ and $△ D C E$ ,
$∠ A C B = ∠ D C E$ (Vertically opposite angles)
$∠ C A B = ∠ C E D$ (Alternate angles to parallel lines AB and DE)
$∠ C B A = ∠ C D E$ (Alternate angle to parallel lines AB and DE)
Thus, $△ A C B ≅ △ E C D$ ,
hence, $\frac{A C}{C E} = \frac{C B}{C D}$ (Corresponding sides)
$\frac{6}{15} = \frac{B C}{C D}$
$\frac{B C}{C D} = \frac{2}{5}$
Let $B C = 2 x$ and $C D = 5 x$
Given $B D = 28$
$B C + C D = 28$
$2 x + 5 x = 28$
$7 x = 28$
$x = 4$
Thus, $B C = 8$ cm and $C D = 20$ cm

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