问题 解答题

类比联想:既然任意一个三角形的三边的垂直平分线交于一点,那三角形的三边上的中线是否也交于一点;三个角的平分线是否也交于一点;试通过折纸或用直尺、圆规画图验证这种猜想.

答案

(1)如图,设△ABC的两条中线BD、CE相交于点G,连接AG并延长交BC于M,作BNCE,连接CN,

∵E是AB的中点,BNCE,

∴点G是AN的中点,

∵点D是AC的中点,

∴GDCN,

∴四边形BNCG是平行四边形,

∴BC、GN互相平分,即点M是BC的中点,AM是BC的中线,即△ABC的三条中线交于一点;

(2)如图,△ABC中,∠A、∠B的平分线交于点P,过P作AB、BC、AC的垂线,垂足分别为D、E、F,

∵AP、BP分别为∠A、∠B的平分线,

∴PF=PD=PE,

∵PF=PE,PE⊥BC,PF⊥AC,

∴点P在∠C的平分线上,

∴三角形的三个内角的角平分线相交于一点.

单项选择题
单项选择题

Americans are often in a hurry. They rush to work, rush home, and rush through their meals. Workers and students usually have only half hour or an hour for lunch. As a result, a lot of Americans go and eat in fast food restaurants. The service is quick, and the prices are cheap.
What do fast food restaurants serve Of course, many of them have hot dogs, hamburgers, fried chicken, pizza, or ice cream. But other fast food restaurants specialize (专门从事) in different foods. Some places serve roast beef. Some serve fish and seafood. In fact, you can find popular foreign dishes in fast food restaurants, too. There are Italian restaurants with Italian sausage (香肠) and spaghetti (通心粉). And there are Chinese restaurants with Cantonese (粤式的) or Sichuan foods.

Which is NOT true about the fast food restaurants in a franchise
[A] Each restaurant has a different owner.
[B] The name of the restaurants is the same both in U.S.A. and other countries.
[C] The food sold everywhere costs the same.
[D] The food tastes the same everywhere.

A lot of fast food restaurants are franchises (产品经销特许权), a very popular form of business in the United States. There are many restaurants in a franchise, and each franchise has a different owner. However, all of the restaurants are under one central management, and the name of the restaurants is the same everywhere in the United States — and in foreign countries, too. This kind of central control guarantees that, for example McDonald’s hamburgers and Kentucky Fried Chicken taste the same everywhere.
In modern American life, fast food restaurants are very important. They provide quick and inexpensive meals for American people in a hurry.