题干

已知△ABC,分别以AB、AC为边作△ABD和△ACE,且AD=AB,AC=AE,∠DAB=∠CAE,连接DC与BE,G、F分别是DC与BE的中点.

(1)如图1,若∠DAB=60°,求∠AFG;如图2,若∠DAB=90°,求∠AFG

(2)如图3,若∠DAB=α,试探究∠AFG与α的数量关系,并给予证明;

(3)如果∠ACB为锐角,AB≠AC,∠BAC≠90°,点M在线段BC上运动,连接AM,以AM为一边以点A为直角顶点,且在AM的右侧作等腰直角△AMN,连接NC;试探究:若NC⊥BC(点C、M重合除外),则∠ACB等于多少度?画出相应图形,并说明理由.(画图不写作法)

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答案(点此获取答案解析)

(1)解:60°;45°
(2)∠AFG=90°-
α
2
证明:连接AG.
∵∠DAB=∠CAE,∴∠DA

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    Children all round the world are familiar with fairy tales such as “The Little Mermaid”(美人鱼), “The Princess and the Pea” and “The Emperor's New Clothes”. The colourful 1 from the stories made us laugh and cry throughout our 2.

    The stories are the creation(创作) of Danish writer Hans Christian Anderson. He was born into a 3 family in Odense, Denmark, on April 2, 1805. His 4 life was not easy. His father was a shoemaker and his mother a washerwoman. He 5 very little education. As a child he was very6 and was laughed at for being feminine (女性化的) and tall.

    In 1816 his father died and Anderson was 7 to go out to work, first in a tailor's shop and 8 at a tobacco factory. 9 the age of 14 Anderson moved to Copenhagen to start a career as a singer and actor. He struggled for three years 10 he had to leave the theatre when his voice 11 in 1822.

    12, Anderson went to a grammar school. Having done well, he was admitted to Copenhagen University in 1828. He began to publish his fairy tales in 1835. They 13 in small volumes (量) until his death.

    14 Anderson lived a 15 life, he tried to make people 16 in all his stories. He wrote because he didn't want children to have a 17 childhood as he did. The works 18 Anderson world fame(声誉), but he remained a 19 man. He never married and his friends were the people who paid for his work. Anderson 20 on August 4, 1875. His home in Odense is now a museum and thousands of people visit it every year.