题干

如图,在△ABC中,∠ACB=90°,BC的垂直平分线DE交BC于D,交AB于E,F在DE上,并且AF=CE.

(1)求证:四边形ACEF是平行四边形;

(2)当∠B满足什么条件时,四边形ACEF是菱形?请回答并证明你的结论.

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答案(点此获取答案解析)

解:(1)∵ED是BC的垂直平分线

∴EB=EC,ED⊥BC,

∴∠3=∠4,

∵∠ACB=90°,

∴FE∥AC,

∴∠1=∠5,

∵∠2与∠4互余,∠1与∠3互余

∴∠1=∠2,

∴AE=CE,

又∵AF=CE,

∴△ACE和△EFA都是等腰三角形,

∴∠5=∠F,

∴∠2=∠F,

∴在△EFA和△ACE中

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阅读下面两封信并回答问题。

Letter A

    Young people are always told that they should make the most of their time, that they will never be as free again. So, my question is — why fill up all this free time with housework?Parents expect their children to get good grades, be good at sports, and be popular with other kids.

    However,there is not enough time in the day to do these things and then do housework as well. It's not fair to expect teenagers to give up their precious time to do boring housework. Parents and children both have jobs. Parents' jobs are in the work-place. Their children's jobs are at school.

    The only difference is that parents get paid and children don't. Parents say that they make their kids do housework to teach them responsibility. But this is just a trick. Parents trick their kids into doing housework because they are lazy.

Yours,

Overloaded

Letter B

    Both parents and children have jobs. The parents' job is to go to work to earn money. The children's job is to go to school. But we all get hungry. Someone has to cook the meals and clean up afterward. We all wear clothes that get dirty. Someone has to wash them, iron them, and put them away. Children work from 9 until 4. Parents work from 8 until 6. Sure, after 4 o'clock, children have homework. But after 6, parents have homework too. They have to do the shopping, go to the bank, pay the bills, and help their kids with their own homework!

    I think it's only fair that teenagers help out a bit at home. They might not like it, but it's good for them.It teaches them how to look after themselves.This is really useful when they leave home to go to college or to live on their own.