题目

如图，AD为△ABC的高，点H为AC的垂直平分线与BC的交点，HC＝AB (1) 如图1，求证：∠B＝2∠C (2) 如图2，若2∠DAF＝∠B－∠C ① 求证：AC＝BF＋BA ② 直接写出的值      答案：证明：(1) 连接AH ∵H为AC的垂直平分线与BC的交点 ∴HA＝HC＝AB ∴∠B＝∠AHC＝2∠C (2) ① 反推AF平分BAC ∵2∠DAF＝∠B－∠C ∴∠DAF＝∠B－∠C 在Rt△ADF中，∠DAF＝90°－∠AFD＝90°－∠FAC－∠C ∴90°－∠FAC－∠C＝∠B－∠C ∴∠FAC＝90°－∠B－∠C＝∠BAC 即AF平分∠BAC 在AC上截取AG＝AB，连接FG ∴△BAF≌△GAF（SAS） In North America, people are always in a hurry. Children have special lessons or sports activities after school. Parents often work late and don’t get home until 7 or 8 o’clock at night. More than 50% of women work at full-time jobs, and many people do part-time work.When a family wants to eat a meal together, often(A) there isn’t enough time to prepare the food. That is why fast food is so popular in North America.(B) People spend about 40% of their money buying fast food.Fast food is the food ____(C)___ pizza, sandwiches or fried chicken. People can buy the food from a restaurant chain(连锁) like Pizza Hut, McDonald’s or KFC. (D) Fast food saves work and time, but it is usually junk food.Fast food is popular in many countries. American fast food companies(公司) now have restaurants all over the world. But not everyone is happy about the spread(扩张)of North American fast food. Some people in Italy want to fight against(抵制) it . (E)They don’t want any more fast food chains to open in their country. They also want to fight against the spread of fast food everywhere in the world.1.将文中( A )处划线部分改写为：A family is usually ________________ busy_______________ prepare the food.2. 把( B )处翻译成汉语。________________________________________________________________3. 把( D )处翻译成汉语。__________________________________________________________________4.在( C )处空白处填入适当的词组_____________________________5.文中划线部分（E）处指代的是________________________________.