Finding the sides with equal angles

In the given figure BA is parallel to CD, $\displaystyle \angle DAC =\angle ABC$. AB = 10cm, BC= 9cm, AC=15cm. What is the length of AD?I tried solving with AB/BC = **AD/AC**. The answer turned out to be wrong because the solution in the book is given as,

*Since $\displaystyle \triangle$ ABC is similar to $\displaystyle \triangle$CAD, therefore, AB/BC = ***AC/AD**.

I did not understand why they considered $\displaystyle \triangle$CAD instead $\displaystyle \triangle$DAC and *AB/BC = ***AC/AD **accordingly.