题干

阅读下面材料:

如图(1),把△ABC沿直线BC平行移动线段BC的长度,可以变到△DEC的位置;

如图(2),以BC为轴,把△ABC翻折180°,可以变到△DBC的位置;

如图(3),以点A为中心,把△ABC旋转180°,可以变到△AED的位置.

像这样,其中一个三角形是由另一个三角形按平行移动、翻折、旋转等方法变成的.这种只改变位置,不改变形状大小的图形变换,叫做三角形的全等变换.

回答下列问题:

①在图(4)中,可以通过平行移动、翻折、旋转中的哪一种方法怎样变化,使△ABE变到△ADF的位置;

②指图中线段BE与DF之间的关系,为什么?

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答案(点此获取答案解析)

解:①在图4中可以通过旋转90°使△ABE变到△ADF的位置.

②由全等变换的定义可知,通过旋转90°,△ABE变到△ADF的位置,只改变位置,不改变形状大小,

∴△ABE≌△ADF.

∴BE=DF,∠ABE=∠ADF.

∵∠ADF+∠F=90°,

∴∠ABE+∠F=90°,

∴BE⊥DF.

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    Wherever she goes, Molly leaves her mark. Without saying a word, she speaks to people with her kind eyes. Even when she walks away, she leaves an impression. Molly's mark is a smile, stamped into the ground by the horseshoe at the bottom of her false leg.

    A few years ago, Molly was badly attacked by a dog. The dog bit all four of Molly's legs and left large cuts in her face. Molly's owner, Kate Harris, took her to an animal hospital. Doctors there were able to save Molly's life, but soon one of her legs became very infected (感染).

    At first, doctors thought Molly would have to be put to sleep. But Molly changed their minds. This pony, doctors noticed, shifted her weight, and rested her good leg from time to time. Doctors knew that Molly had amazing intelligence, and that she wanted to live.

    Several doctors operated on Molly, and removed her infected leg. A false leg was made for her. The leg was a hollow cast with a pole at the bottom for balance. Doctors gave Molly a special horseshoe at the bottom of the leg. This horseshoe she had had a stamp of a smile face in it!

    After the operation, Molly walked around on all four legs, as if nothing had ever happened to her! Now, with every step she takes, she stamps a smile in the dirt. But she leaves her mark in other ways, too.

    Kaye Harris took Molly to the false leg center. There were children there who, like Molly, had artificial arms or legs. They were amazed to see a pony with a false leg. Molly made them smile and gave them hope. Soon, Molly began to visit schools, nursing homes, army bases and hospitals. A book was even written about Molly!