题目

如图 ，已知中，AB=BC ，，点 为斜边 的中点，连接，AF是 的平分线，分别与 BD、相交于点 E、F ． （1） 求证： ； （2） 如图 ，连接,在不添加任何辅助线的条件下，直接写出图中所有的等腰三角形(不包含 ）． 答案：证明：∠ABC=90∘，BA=BC，点D为斜边AC的中点， ∴BD⊥AC,∠DBC=45°， ∵AF是∠BAC的平分线， ∴∠BAF=22.5°， ∴∠BFE=67.5°， ∴∠BEF=180°−∠EBF−∠EFB=67.5°， ∴∠BFE=∠BEF， ∴BE=BF； 解：∵∠ABC=90°，BA=BC，点D为斜边AC的中点， ∴BD=AD=CD， ∴△ABD、△CBD是等腰三角形， 由已知得，△ABC是等腰三角形， 由(1)阅读下面文章，根据要求回答下列问题。                                                  British English and American English      Many students want to know the differences between American English and British English. Written Englishis more or less the same in both Britain and America, though there are some spelling differences. For example, the words colour, centre and travelled are spelt color, center, and traveled in American English.      The differences in the spoken language are greater. For example, Americans say dance /dns/, and in southernEngland they say /da:ns/. In America, they pronounce not./nt/, in southern England they say /not/. However,most of the time, people from the two countries do not have any difficulty in understanding each other.      How did these differences come from? There is no quick answer to this question. When people from Englandtravelled to other countries they took the English language with them. At first, the language stayed the same as the language used in Britain, but slowly the language began to change from one part of the world.      Sometimes, the English spoken in America or Canada or Australia changed, but sometimes the languagespoken in these places stayed the same while the language in England changed. For example, 300 years ago, theEnglish talked about "autumn". But Americans still talk about "fall" just as people do in some parts of western England. In the same way Americans use the expression "I guess" (meaning "I think") just as the British did 300years ago.      A great many words and expressions have come into the language from American English, for example movie, gas, store, mail, right away (at once), way of life and so on.      American English has changed over the centuries, too. There are several reasons for this. One of the reasonsis that people travelled to America from all the European countries and from other parts of the world, too. Theystarted to use English, but they also brought in some words from old French. One of the States in the USA is called "Florida". In Spanish this is "the land of flowers". There are a great many American Indian words, for example, "to howl" means "to cry". And "cookbook" is a German word. 根据文章内容判断下列句子的对(T)与错(F)。 (     )1. There are some differences between British and American English. So people from the two countries             can hardly understand each other when talking to each other. (     )2. As time goes by, the English language stays the same. (     )3. Americans usually use "fall" instead of "autumn" when they talk about the seasons.(     )4. "Florida" means"the land of flowers" in American English. (     )5. People who travel to the USA add more words to American English. 根据文章内容，回答下列问题。 6. Which of the following words belongs to British English: movie, gas, mail or petrol?     _______________________________________________________________________________7. Please give the American way of spelling of the following words: colourful, metre and traveller.      _______________________________________________________________________________