题目

如图，D是等边三角形ABC内一点，将线段AD绕点A顺时针旋转60°，得到线段AE，连接CD，BE． （1）求证：∠AEB=∠ADC； （2）连接DE，若∠ADC=105°，求∠BED的度数． 答案：【考点】旋转的性质；等边三角形的性质． 【分析】（1）由等边三角形的性质知∠BAC=60°，AB=AC，由旋转的性质知∠DAE=60°，AE=AD，从而得∠EAB=∠DAC，再证△EAB≌△DAC可得答案； （2）由∠DAE=60°，AE=AD知△EAD为等边三角形，即∠AED=60°，继而由∠AEB=∠ADC=105°可得． 【解答】解：（1）∵△ABC是等边三角形 　　The word“hobby”is an interesting word. Every person has one thing he or she likes to do for fun. Some people like to collect things like stamps or story books. Others like to play football or go window shopping where you can look at many beautiful things without buying them. 　　I have many hobbies I do for fun. I sometimes play golf with my sons. I play tennis with all the family. I like to collect music books. I also collect music instruments（乐器）from China like the erhu , the dizi and the suona. These are the instruments of China which cannot be found in America. 　　My favourite hobby is fishing. I like to go and see my brother in the state of Alaska where fishing is wonderful. We take a boat and go to a small river where we fish for salmon, American's most famous fish. (1)The word“hobby”means ________. [　　] A．collecting stamps B．playing tennis with your friends C．something you enjoy doing in your free time D．something you can see at the window shopping (2)What's the writer's most liked hobby? [　　] A．Playing golf with his sons. B．Fishing. C．Collecting Chinese musical instruments. D．Collecting music books. (3)Salmon is ________. [　　] A．a river where people can go fishing B．a town near Alaska C．a kind of instrument D．a kind of fish