题干

已知:如图,△ABC中,∠ABC=45°,CD⊥AB于D,BE⊥AC于E,BE与CD相交于点F.

求证:BF=AC.

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答案(点此获取答案解析)

证明:∵CD⊥AB,∴∠BDC=∠CDA=90°;∵∠ABC=45°,∴∠DCB=∠ABC=45°(三角形的内角和定理),∴DB=DC(等角对等边);∵BE⊥AC,∴∠AEB=90°,∴∠A+∠ABE=90°(直角三角形的两个锐角互为余角);∵∠CDA=90°,∴∠A+∠ACD=90°,∴∠ABE=∠ACD(同角的余角相等);在△BDF和△CDA中,{

同类题1

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。

D

    Do you know when restaurants were invented? The first restaurant were invented thousands of years ago. However, they were very different from restaurants today.

    The first restaurants were in ancient Greece and ancient Rome. These restaurants served food in large stone bowls people didn't order food from a menu. Everyone used to share the food from big bowls. People believe that these places were very popular because most homes in ancient Greece and Rome did not have kitchens. Also, people didn't have to store food at home if they ate their meals at these restaurants.

    Later, restaurant began to open in China. In the early 1100s, more than one million people lived in the city of Hangzhou, China. It was a very busy city, and people had money. All of these people had to eat. Smart cooks started cooking and selling food along the Imperial Way, a very big street in the city. Unlike in ancient Greece and Rome, people in China could choose food from a menu. They didn't have to eat the same food as everyone else.

    For the next several centuries, there were restaurants all over the world. People could buy food on the street or at inns-- small hotels. Then in the middle of the 1700s, restaurants started opening in Paris. These restaurants were more similar to restaurants we know today. There was a bigger variety of food, and eating in these restaurants was a more enjoyable experience. In the 19th century, trains made travel much faster and simpler. In the end, this kind of restaurant began to appear all over Europe and in other parts of the world.

    Now, restaurants are everywhere. You can buy a variety of different kinds of food. You can have food sent to your door. But remember it wasn't always like that.

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阅读下面的文言文,完成小题。

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(节选自《新唐书·魏知古传》)