试题与答案

【原创】下列命题正确的有 ( )个 ①400角为内角的两个等腰三角形必相似 ②若

题型:选择题

题目:

【原创】下列命题正确的有 (      )个

①400角为内角的两个等腰三角形必相似

②若等腰三角形一腰上的高等于腰长的一半,则这个等腰三角形的底角为750

③一组对边平行,另一组对边相等的四边形是平行四边形

④一个等腰直角三角形的三边是a、b、c,(a>b=c),那么a2∶b2∶c2=2∶1∶1

⑤若△ABC的三边a、b、c满足a2+b2+c2+338=10a+24b+26c,则此△为等腰直角三角形。

A.1个

B.2个

C.3个

D.4个

答案:

答案:A

分析:根据三角形的内角和定理,平行四边形的判定定理,相似三角形的判定定理,等腰三角形的性质,等腰直角三角形的性质,配方法的应用对5个结论逐一分析即可.

解答:解:①40°角为内角两个等腰三角形有2种情况,

一是顶角为40°的一个等腰三角形,二是底角为40°的一个等腰三角形,那么这两个三角形不相似,所以此结论不正确;

②高在内部时,顶角为30度,底角75度高在外部时,顶角的外角30度,底角15度.所以有2种情况:15度或75度,所以此结论不正确;

③一组对边平行,另一组对边相等的四边形也可以是梯形,所以此结论不正确;

④∵一个等腰直角三角形的三边是a、b、c,(a>b=c),

∴a为等腰直角三角形的斜边,

∴a2=2b2=2c2

∴a2:b2:c2=2:1:1;

∴此结论正确;

⑤∵a2+b2+c2=10a+24b+26c-338,∴(a-5)2+(b-12)2+(c-13)2=0,

∴a-5=0,b-12=0,c-13=0,即a=5,b=12,c=13.

∵52+122=132

∴△ABC是直角三角形.而不是等腰直角三角形.

∴此结论不正确;

因此命题正确的有1个.

故选A.

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                                                                     Travel and Life

     Millions of people all over the world spend their holidays travelling. They travel to see other countries and

continents, modern cities and the ruins of ancient tombs; they travel to enjoy particular places, or just for a

change of scene. It's always interesting to discover new things, different ways of life, to meet different people,

to try different food and to listen to different music.

     Those who live in the country like to go to a big city and spend their time visiting museums and art galleries

(艺术馆), looking at shop windows and dining at exotic (异国情调的) restaurants. City dwellers usually like a

quiet holiday by the sea or in the mountains, with nothing to do but walk, bathe and laze in the sun.

     Most travellers and holiday-makers take a camera with them and take pictures of everything that interests

them-the sights of a city, old churches and castles, views of mountains, lakes, valleys, plains, waterfalls, forests,

different kinds of trees, flowers and plants, animals and birds. Later, perhaps years later, they will be reminded

by the photos of the happy time they have had.

     People travel by train, by plane, by boat and by car. All means of travel have their advantages and

disadvantages. And people choose one according to their plans and destinations.

     If we are fond of travelling, we will see and learn a lot of things that we can never see or learn at home,

though we may read about them in books and newspapers, and pictures of them on TV. The best way to study

geography is to travel, and the best way to get to know and understand people is to meet them in their own

homes.

1. What is the main idea of the first paragraph?

A. Why do so many people like to travel?

B. Who like traveling most of all?

C. What form of transport can people choose when travelling?

D. Why do different people have different preferences when travelling?

2. While travelling, people can do all the following except ____.

A. experiencing new things and different ways of life

B. doing window shopping and dining at foreign restaurants

C. taking photos of what they are interested in

D. being reminded by the photos of the happy time they have had

3. The best way to study geography is ____.

A. to travel to places and experience it for yourself

B. to read books and newspapers about geography

C. to watch geographical programmes on TV at home

D. to learn about it from your geography teachers at school

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