三角形易错题集锦(带答案)

三角形易错题集锦(带答案)
三角形易错题集锦(带答案)

三角形易错题

一、填空题(共10小题)(除非特别说明,请填准确值)

1.一个凸多边形最小的一个角为100°,其他的角依次增加10°,则这个多边形的边数为_________.2.等腰三角形ABC的周长是8cm,AB=3cm,则BC=_________cm.

3.等腰三角形的周长为20cm,若腰不大于底边,则腰长x的取值围是_________.

4.如图:a∥b,BC=4,若三角形ABC的面积为6,则a与b的距离是_________.

5.小亮家离学校1千米,小明家离学校3千米,如果小亮家与小明家相距x千米,那么x的取值围是_________.

6.已知△ABC两边长a,b满足,则△ABC周长l的取值围是_________.7.若等腰△ABC(AB=AC),能用一刀剪成两个等腰三角形,则∠A=_________.

8.图1是一个三角形,分别连接这个三角形三边的中点得到图2;再分别连接图2中间小三角形的中点,得到图3.(若三角形中含有其它三角形则不记入)

(1)图2有_________个三角形;图3中有_________个三角形

(2)按上面方法继续下去,第20个图有_________个三角形;第n个图中有_________个三角形.(用n的代数式表示结论)

9.一个三角形两边长为5和7,且有两边长相等,这个三角形的周长是_________.

10.两边分别长4cm和10cm的等腰三角形的周长是_________cm.

参考答案与试题解析

一、填空题(共10小题)(除非特别说明,请填准确值)

1.一个凸多边形最小的一个角为100°,其他的角依次增加10°,则这个多边形的边数为8.

考点:多边形角与外角.

专题:计算题.

分析:根据角和公式,设该多边形为n边形,角和公式为180°?(n﹣2),因为最小角为100°,又依次增加的度数为10°,则它的最大角为(10n+90)°,根据等差数列和的公式列出方程,求解即可.解答:解:设该多边形的边数为n.

则为=180?(n﹣2),

解得n1=8,n2=9,

n=8时,10n+90=10×80+90=170,

n=9时,10n+90=9×10+90=180,(不符合题意)

故这个多边形为八边形.

故答案为:8.

点评:本题结合等差数列考查了凸n边形角和公式.方程思想是解此类多边形有关问题常要用到的思想方法,注意凸n边形的角的围为大于0°小于180°.

2.等腰三角形ABC的周长是8cm,AB=3cm,则BC=2或3或2.5cm.

考点:等腰三角形的性质;三角形三边关系.

专题:计算题.

分析:按照AB为底边和腰,分类求解.当AB为底边时,BC为腰;当AB腰时,BC为腰或底边.解答:解:(1)当AB=3cm为底边时,BC为腰,

由等腰三角形的性质,得BC=(8﹣AB)=2.5cm;

(2)当AB=3cm为腰时,

①若BC为腰,则BC=AB=3cm,

②若BC为底,则BC=8﹣2AB=2cm.

故本题答案为:2或3或2.5cm.

点评:本题考查了等腰三角形的性质,分类讨论思想.关键是明确等腰三角形的三边关系.

3.等腰三角形的周长为20cm,若腰不大于底边,则腰长x的取值围是5<x≤.

考点:等腰三角形的性质;三角形三边关系.

分析:根据题意以及三角形任意两边之和大于第三边列出不等式组求解即可.

解答:解:等腰三角形的底边为20﹣2x,

根据题意得,,

由①得,x≤,

由②得,x>5,

所以,腰长x的取值围是5<x≤.

故答案为:5<x≤.

点评:本题考查了等腰三角形两腰相等的性质,三角形的三边关系,列出不等式组是解题的关键.4.如图:a∥b,BC=4,若三角形ABC的面积为6,则a与b的距离是3.

考点:平行线之间的距离;三角形的面积.

分析:过A作AD⊥BC于D,则AD的长就是a b之间的距离,根据三角形的面积公式求出AD即可.解答:

解:

过A作AD⊥BC于D,

∵三角形ABC的面积为6,BC=4,

∴×BC×AD=6,

×4×AD=6,

AD=3,

∵a∥b,

∴a与b的距离是3,

故答案为:3.

点评:本题考查了两条平行线间的距离和三角形的面积,关键是正确作辅助线后能求出AD的长.

5.小亮家离学校1千米,小明家离学校3千米,如果小亮家与小明家相距x千米,那么x的取值围是2≤x≤4.

考点:三角形三边关系.

分析:小明、小亮家的地理位置有两种情况:

(1)小明、小亮家都在学校同侧;

(2)小明、小亮家在学校两侧.

联立上述两种情况进行求解.

解答:解:(1)小明、小亮家都在学校同侧时,x≥2;

(2)小明、小亮家在学校两侧时,x≤4.

因此x的取值为2≤x≤4.

点评:本题注意考虑两种不同的情况,能够分析出每一种情况的围,再进一步综合两种情况的结论.6.已知△ABC两边长a,b满足,则△ABC周长l的取值围是6<l<10.

考点:非负数的性质:算术平方根;非负数的性质:偶次方;三角形三边关系.

分析:

由,可得+(b﹣3)2=0,则a=2,b=3,可得第三边c的取值围是1<c<5,从而求得周长l的取值围.

解答:

解:∵,

∴+(b﹣3)2=0,

∴a=2,b=3,

∴第三边c的取值围是1<c<5,

∴△ABC周长l的取值围是6<l<10.

故答案为:6<l<10.

点评:此题主要考查了非负数的性质,其中首先灵活应用了非负数的性质,然后利用三角形三边之间的关系,难度中等.

7.若等腰△ABC(AB=AC),能用一刀剪成两个等腰三角形,则∠A=36°或90°或108°.

考点:等腰三角形的性质;三角形角和定理.

分析:题中只说是等腰三角形,没有指明该等腰三角形的形状,故应该分三种情况进行分析.

解答:解:(1)当顶角为锐角时,

①∵剪后AB=AC,AD=BD=BC,∠C=∠ABC=∠BDC=2∠A.

∴∠A+∠C+∠ABC=5∠A=180°

∴∠A=36°

②当AB=AC,AD=BD,BC=CD时

可求出∠A=;

(2)当顶角为钝角时,

∵剪后AB=AC,AC=CD,BD=AD,∠C=∠B=∠BAD=∠ADC=∠DAC

∴∠B+∠C+∠BAD+∠DAC=5∠C=180°

∴∠C=36°

∴∠BAC=108°

(3)当顶角为直角时,

∵剪后AB=AC,CD=AD=BD,∠B=∠C=∠CAD=∠BAD=45°

∴∠CAB=90°

所以填∠A为36°、或90°或108°.

点评:本题考查了等腰三角形的性质及三角形角和定理;分情况讨论的正确应用时解答本题的关键.

8.图1是一个三角形,分别连接这个三角形三边的中点得到图2;再分别连接图2中间小三角形的中点,得到图3.(若三角形中含有其它三角形则不记入)

(1)图2有5个三角形;图3中有9个三角形

(2)按上面方法继续下去,第20个图有77个三角形;第n个图中有(4n﹣3)个三角形.(用n的代数式表示结论)

考点:三角形.

专题:规律型.

分析:正确数一下(2)(3)中,三角形的个数,可以得到(3)比(2)增加了4个三角形,同理(4)比(3)增加了4个三角形,依此类推即可求解.

解答:解:(1)图2有5个三角形;图3中有9个三角形;

(2)按上面方法继续下去,可以得到(4)比(3)增加了4个三角形,

依此类推,第20个图有1+(20﹣1)×4=77个三角形;第n个图中有4(n﹣1)+1=4n﹣3个三角形.

点评:正确观察图形得到规律是解决本题的关键,解决这类题的方法是根据题目的叙述,求出几个图形中三角形的个数,从而求出规律.

9.一个三角形两边长为5和7,且有两边长相等,这个三角形的周长是17或19.

考点:三角形三边关系.

分析:腰长为5时,得到三条线段;腰长为7时,得到三条线段.若较短的两边条线段之和大于最长的一条线段,那么能组成三角形,让三边相加即可.

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定语从句 一、单项选择 1.All the neighbors admire this family, _________ the parents are treating their child like a friend. A.why B. where C. which D. that 2.It was an exciting moment for these football fans this year, __________ for the first time in years their team won the World Cup. A.that B. while C. which D. when 3.By serving others, a person focuses on someone other than himself or herself, _____ can be very eye-opening and rewarding. A.who B. which C. what D. that 4.Anyway, that evening,_______ I’ll tell you more about later, I ended up staying at Rachel’s place. A.when B. where C. what D. which 5.Those successful deaf dancers think that dancing is an activity _____ sight matters more than hearing. A.when B. whose C. which D. where 6.Great changes have taken place in that school. I t’s no longer ______ it was 20 years ago, ______ it was so poorly equipped. A.what; when B. that; which C. what; which D. which; that 7.By nine o’clock, all the Olympic torch bearers had reached the top of Mount Qomolangma, ______ appeared a rare rainbow soon. A.of which B. on which C. from which D. above which 8.The boss ____department Mrs. King worked 10 years ago looked down upon women. A.in which B. in that C. in whose D. whose 9.The journey around the world took the old sailor nine months, _____ the sailing time was 226 days. A.of which B. during which C. from which D. for which 10.For many cities in the world, there is no room to spread out further, ____New York is an example. A.for which B. in which C. of which D. from which https://www.360docs.net/doc/7f562116.html,ter cases will be introduced to readers ____consumer complaints have resulted in changes in the law. A.where B. when C. who D. which 12.The doctor advised Vera strongly that she should take a holiday, but ____ didn’t help. A.it B. she C. which D. he 13.He has two children, both of ____ being abroad. A.them B. which C. whom D. who 14.-Mom, what did your doctor say?

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