如图，在梯形ABCD中，AD∥BC，对角线AC、BD相交于点O，问△AOB与△COD是否相似？有一位同学解答下：

∵AD∥BC，

∴∠ADO=∠CBO，∠DAO=∠BCO．

∴△AOD∽△BOC．

∴$\frac{AO}{BO}=\frac{DO}{CO}$．

又∵∠AOB=∠DOC，

∴△AOB∽△COD．

请判断这位同学的解答是否正确并说明理由．

阅读理解
    A beautiful and very successful actress was the star for a new musical show. Her home was in the country, but she didn't want to go back there every night, so she bought an expensive house in the center of the city, got some beautiful furniture and got a man to paint the rooms in new colour.
    It was very difficult to get tickets for her show in the evening, because everyone wanted to see it. So she decided to give the painter two of the best seats. She hoped that this would make him work better for her. He took the tickets without saying anything, and she heard no more about them until the end of month, when she got the painter's bill. At the bottom of it were these words: “Four hours from 5:00 p.m. to 9:00 p.m. watching Miss Hall sing and dance: 3 pounds,”with this note: “Before 5:00 p.m. I get 10 shillings (先令)an hour and after 5:00 p.m. 15 shillings.”