问题 选择题

△ABC中,∠ABC=30°,边AB=10,边AC可以从4,5,7,9,11取一值.满足这些条件的互不全等三角形的个数是(  )

A.6

B.7

C.5

D.4

答案

答案:A

题目分析:根据含30°的直角三角形的性质可知取5的时候是AC垂直于AB,也就是AC能取的最小值.

当AC=5时,AC=AB,此时∠ACB为直角,有1个三角形为直角三角形;

当AC=7时,∠ACB为钝角或锐角时,各有1个,共2个;

当AC=9时,∠ACB为钝角或锐角时,各有1个,共2个;

当AC=11时,∠ACB为锐角时,有1个,此时不存在∠ACB为钝角的三角形;

综上所述,共有6个满足条件的互不全等三角形.

故选A.

点评:解题的关键是熟练掌握含30°的直角三角形的性质:直角三角形中30°的锐角所对的直角边等于斜边的一半.

阅读理解

第三部分:阅读理解 (共20小题;每小题2分, 满分40分)

阅读下列短文,从每题所给的四个选项(A、B、C和D)中,选出最佳选项。

When you look at a map of the Caribbean, you will see a bunch of little islands surrounded by. Blue waters, which include places that aren't always household names like Montserrat and Anguilla.

While some of the names may not be familiar, the fact is that the Caribbean is a popular vacation region. Those little clots on the map often turn out to be island paradises. There are more than 7,000 islands, islets, and reefs in the area, many of which are lightly populated and stunningly beautiful.

The biggest challenge you might face in planning your trip is choosing where in the Caribbean to go. All of the nations feature excellent weather. Most feature beautiful beaches. You can enjoy the waters in most of the Caribbean nations and as is often the case with island nations, you will be welcomed warmly by the locals. Here are some resources to help you.

Unless you can walk on water or you cruise the Caribbean, the best way to visit is to fly. Some destinations have more frequent and cheaper flights than others. You should do some comparison shopping on flights to the Caribbean. And if you are planning on flying there during the Christmas holiday weeks it's important to book as early as possible because prices will just keep going up as they get closer.

The Caribbean offers a wide variety of accommodation options. Check out the Caribbean hotels that are available to get a better idea of the various options. If you are on a tight budget then, the Caribbean could be challenging, as there are only a few cheap hotels and hostels that might help you save some money.

Many people see the Caribbean from a cruise ship. There is no shortage of cruises that will take you through the region. Cruise and Vacation Travel Packages is the place to go to find the cruise or vacation package that is right for you.

56. The Caribbean is popular with tourists because ________.

A. the area has a small population             B. the area has a long history.

C. there are many beautiful islands there             D. tire area is very developed

57. The underlined word "they" in the fourth paragraph refers to _________.

A. prices of air tickets                           B. tourists to the Caribbean

C. flights to the Caribbean                  D. the Christmas holiday weeks

58. Which of the following statements is NOT true according to the passage?

A. The weather in all of the Caribbean nations is fine.

B. Most of the Caribbean hotels are cheap.

C. The local people of the Caribbean are very friendly.

D. It is hard to choose a destination in the Caribbean.

单项选择题