题干

如图,AB和CD相交于点O,∠C=∠1,∠D=∠2,求证:∠A=∠B.

证明:∵∠C=∠1,∠D=∠2(已知)

又∵∠1=∠2(____ )

____ (____ )

∴AC∥BD(____ )

____ (两直线平行,内错角相等)

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答案(点此获取答案解析)

对顶角相等,∠C=∠D,等量代换,内错角相等,两直线平行,∠A=∠B

同类题1

文言文阅读,阅读下面的文言文,完成问题。

    梅之焕,字彬父,麻城人,侍郎国桢从子也。年十四为诸生。御史行部阅武,之焕骑马突教场。御史怒,命与材官角射,九发九中,长揖上马而去。万历三十二年举进士,改庶吉士。居七年,授吏科给事中。东厂太监李浚诬拷商人,之焕劾其罪。寻上言:“今天下民穷饷匮,寇横兵疲。言官舍国事争时局,部曹舍职掌建空言,天下尽为虚文所束缚。有意振刷者,不日生事,则日苛求。事未就而谤兴,法未伸而怨集,豪杰灰心,庸人养拙,国事将不可为矣。请陛下严综核以责实事,通言路以重纪纲,别臧否以惜人才,庶于国事有济。”时朝臣部党角立,之焕廉觚自胜,尝言:“附小人者必小人,附君子者未必君子。蝇之附骥,即千里犹蝇耳。”天启元年以通政参议召迁太常少卿,擢右佥都御史,巡抚南、赣。丁内外艰,家居。当此之时,魏、客乱政,应山杨涟首发忠贤之奸。忠贤恚甚,拷杀涟。由此悍然益诛锄善类。谓涟被逮时过麻城涟罪人也之焕与盘桓流涕当削籍其实涟未尝过麻城也无何逆党梁克顺诬以赃私诏征赃。庄烈帝即位,乃免征,起故官,巡抚甘肃。大破套寇,斩首七百余级,生得部长三人,降六百余人。明年春,寇复大入,患豌豆创,环大黄山而病。诸将请掩之,之焕不可曰:“幸灾不仁,乘危不武,不如舍之,因以为德焉。”遂不战。逾月,群寇望边城涕泣而去。冬,京师戒严,有诏入卫。且行,西部乘虚犯河西。之焕止留,遣兵伏贺兰山后,邀其归路,大兵出水泉峡口,再战再败之,斩首八百四十有奇,引军东。明年五月抵京师,已后时矣,有诏之焕入朝。翌日又诏之焕落职候勘,温体仁已栖政矣。初,体仁讦钱谦益,之焕移书中朝,右谦益。至是,体仁修隙,之焕遂得罪。之焕虽文士,负材武,善射,既废,无所见。所居县,阻山多盗。之焕无事,辄率健儿助吏捕,无脱者。先是,甘肃兵变,其溃卒畏捕诛,往往亡命山谷间,为群盗,贼势益张。至是,贼数万来攻麻城,望见之焕部署,辄引去。帝追叙甘肃前后功,复之焕官,荫子,然终不召。明年病卒。

(节选自《明史•梅之焕传》)


【注】①豌豆创:天花。

同类题2

根据短文理解,选择正确答案。

    A student was one day taking a walk with his teacher. As they went along, they saw a pair of old shoes lying in the path. They were a poor farmer's, who was working in the nearby field.

    The student turned to the teacher, saying: “we will hide his shoes, and hide ourselves behind those trees, and wait to see what he will do.”

    “My young friend,” answered the teacher, “we should never make fun of the poor. Why not put a coin in each shoe, and then we will hide ourselves and watch?” The student did so and they both hid themselves behind the trees. The poor man soon finished his work, and came across the field to the path where he had left his coat and shoes.

    After putting on his coat, he put his foot into one of his shoes, and felt something hard. Then he bent (弯腰) down to feel what it was, and found the coin. Surprised, he looked at the coin, turned it around and looked at it again. He then looked around, but no person was seen. He put the money into his pocket, and continued to put on the other shoe. His surprise was doubled on finding the other coin.

    He couldn't control his feelings and fell to his knees, looked up to the sky and expressed his thanks. Then he spoke of his wife, sick and helpless, and his children without bread. He said the help would save them from dying.

    The student stood there deeply moved, and his eyes filled with tears. “Now,” said the teacher, “are you not much happier than if you had hidden the shoes?”

同类题3

阅读下文,回答相关问题。

        李疑者,居通济门外,闾巷子弟执业造其家,得粟以自给。故贫甚,然独好周人急。金华范景淳吏吏部,得疾,无他子弟。人殆之,不肯舍。杖踵疑门,告曰:“我不幸被疾,人莫舍我。闻君义甚高,愿假榻。”疑许诺,延就坐,汛室,具床褥炉灶居之,征医师视脉,躬为煮糜炼药,旦暮执手问所苦。既而疾滋甚,不能起,溲矢污衾席,臭秽不可近。疑日为刮摩浣涤,不少见颜面。景淳流涕曰:“我累君矣。恐不复生,无以报厚德,囊有黄白金四十余两,在故旅邸,原自取之。”疑曰:“患难相恤,人理宜尔,何以报为!”景淳曰:“君若不取,我死,恐为他人得,何益?”疑遂求其里人偕往,携而归,面发囊,志其数而封识之。数日,景淳竟死,疑出私财,买棺殡于城南聚宝山。举所封囊寄其里人家,往书召其二子至。及二子至,取囊按籍而还之。二子以米馈,却弗受,反遗以货,遣归。
        士大夫咸喜与疑交。见疑者皆曰:“善士,善士!”太史氏曰:吾与疑往来,识其为人,非有奇伟壮烈之姿也,而其所为事乃有古义勇风。语曰举世混浊,清士乃见。吾伤流俗之嗜利也,传其事以劝焉。”
      【注】①执业:指捧书求教,犹言受业。②汛室:汛,洒水。汛室,指打扫房间。