题干

如图设M为线段AB中点,AE与BD交于点C,∠DME=∠A=∠B=α,且DM交AC于F,EM交BD于G.

(Ⅰ)写出图中三对相似三角形,并对其中一对作出证明;

(Ⅱ)连结FG,设α=45°,AB=4 2 ,AF=3,求FG长.

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答案(点此获取答案解析)

解:(I)根据相似三角形的判定定理可得:△AME∽△MFE,△BMD∽△MGD,△AMF∽△BGM.

对△AMF∽△BGM给出以下证明:

∵∠AMD=∠B+∠BDM,∠BGM=∠DMG+∠BDM,又∠B=∠A=∠DME=α,

∴∠AMF=∠BGM,∴△AMF∽△BGM.

(II)由(I)可得:△AMF∽△BGM,∴

同类题2

任务型阅读

    Many times we tend to use our hands to explain our needs and thoughts.____So you must be cautious when using hand gestures in communication.

    Hand gestures are a way of communicating with others and conveying your feelings. These gestures are most helpful when one is speaking to someone with no language in common. The meanings of hand gestures in different cultures may translate into different things.____Former President George W. Bush had to face a major faux pas(失礼) during a visit to Australia. He tried to signal a peace sign by waving the two-finger or V-sign at the crowd.

    You may think of this as a simple gesture, but he committed a major error.____The meaning of this hand gesture in Australia was asking the crowd to screw themselves, a rude expression used to show you're very angry!____Therefore, it is very important to understand the meanings of gestures before you travel to different countries.

    ____Those considered as good gestures in one country may be termed as offensive gestures in some countries. So, if you are a frequent flier to different countries, improve your communication skills by learning the meaning of hand gestures.

A. Here is a very common example.

B. Instead of his palm facing outwards, it faced inwards.

C. The great man received warm welcome by the Australians.

D. We communicate not only by words, but by hand gestures as well.

E. A serious error committed by the then most powerful man in the world.

F. But the same hand gesture may mean something quite offensive to a person from a different cultural background.

G. Before you communicate with people in different cultures, you need to understand the meaning of gestures.

同类题5

阅读下文,完成后面小题。

为爱挺直

郭华悦

    ①父亲早早去世,为了生计,母亲在家乡摆了个水果摊,每天天没亮就要起来张罗。到了七点左右,一切准备妥当了,于是用三轮的脚踏车,载着顺路的他和一车水果,在晨曦中一路奋进。

    ②母亲的背驼得很严重。到了冬天,在这个北方的小城里,北风裹着雪花,一路肆虐。每当这个时候,母亲总是用力地挺直了背。躲在母亲背后的他,恍然发现母亲的驼背直了不少。

    ③到了学校,他欢呼着跳下车,把这个惊喜发现告诉了母亲。他还沾沾自喜地叮嘱母亲,说不定蹬脚踏车有助于纠正驼背呢。母亲笑了笑,不以为意。可是懵懂的他却天真地认为,如果母亲能直起背来,自己就不会被同学叫做“小罗锅”了。

    ④母亲蹬脚踏车挺直的脊背,让他看到了希望。可是日复一日,他失望地发现,母亲蹬脚踏车时,脊背是直的,可一下车,却又成了驼背。于是,同学们的嘲笑始终伴随着他。

    ⑤后来,他考上了大学,毕业后,留在了城市里。没过了几年,他娶了个漂亮的妻子,也增添了一个可爱的小生命。母亲一直想过来看看孙女,可是他碍于面子,始终说自己忙,不断推脱。

    ⑥直到有一天,他骑着自行车,送四岁的女儿去幼儿园。那天的北风格外地大,刮在脸上竟有些生疼。女儿惊叫了几声,他于是下意识地挺直脊背,挡住迎风而来的寒风。风像刀子一样,在身上刮过,他却始终牵挂着后座上的女儿。

    ⑦那一刻,他突然想起了老家的母亲。他也终于明白,那些风雨交加的早上,母亲奋力地挺直了一直被他嫌弃的驼背,为后座的他挡住了刺骨的风雪。母亲的背,因为爱而挺直。可他不知道的是,每次把他送到学校,回到水果摊后,母亲的背总会疼上大半天。这样的戏,在他年少时光中,日复一日的上演。

    ⑧他的心里,突然涌进了阵阵酸楚。母亲的背是驼的,爱却很直。每个子女的身前,都有一堵挡风遮雨的挺直脊背,那是一堵爱的厚墙。