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【323647】2023七年级数学上册 第5章 相交线与平行线5.2 平行线5.2.2平行线的判定训练

时间:2025-01-15 19:29:00 作者: 字数:2742字
简介:

5.2.2 平行线的判定

(检测时间50分钟 满分100)

班级_________________ 姓名____________ 得分________

一、选择题:(每小题3,15)

1.如图1所示,下列条件中,能判断AB∥CD的是( )

A.∠BAD=∠BCD B.∠1=∠2; C.∠3=∠4 D.∠BAC=∠ACD

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

(1) (2) (3)

2.如图2所示,如果∠D=∠EFC,那么( )

A.AD∥BC B.EF∥BC C.AB∥DC D.AD∥ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> EF

3.如图3所示,能判断AB∥CE的条件是( )

A.∠A=∠ACE B.∠A=∠ECD C.∠B=∠BCA D.∠B=∠ACE

4.下列说法错误的是( )

A.同位角不一定相等 B.内错角都相等]

C.同旁内角可能相等 D.同旁内角互补,两直线平行

5.不相邻的两个直角,如果它们有一边在同一直线上,那么另一边相互( )

A.平行 B.垂直 C.平行或垂直 D.平行或垂直或相交

二、填空题:(每小题3,9)

1.在同一平面内,直线a,b相交于P,a∥c,bc的位置关系是______.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> 2.在同一平面内,若直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> a,b,c满足a⊥b,a⊥c,bc的位置关系是______.

3.如图所示,BEAB的延长线,量得∠CBE=∠A=∠C.

(1)由∠CBE=∠A可以判断______∥______, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> 根据是_________.

(2)由∠CBE=∠C可以判断______∥______,根据是_________.

三、训练平台:(每小题15,30)

  1. 如图所示,已知∠1=∠2,AB平分∠DAB,试说明DC∥AB.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

  1. 如图所示,已知直线EFAB,CD分别相交于K,H,EG⊥AB,∠CHF=600,∠E=­30°,试说明AB∥CD.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

四、提高训练:(20)[

如图所示,已知直线a,b,c,d,e,且∠1=∠2,∠3+∠4=180°,ac平行吗?­什么?

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> [来源:学科网]

五、探索发现: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> (22)

如图所示,请写出能够得到直线AB∥CD的所有直接条件.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> 、中考题与竞赛题:(4)

(江苏) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> 图所示,直线a,b被直线c所截, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> 给出下列四个条件:①∠1=∠­5;②∠1=∠7;③∠2+∠3=180°;④∠4=∠7.其中能说明a∥b的条件序号为( )

A.①② B.①③ C.①④ D.③④







答案:

一、1.D 2.D 3.A 4.B 5.A

二、1.相交 2.平等 3.(1)AD BC 同位角相等,两直线平行 (2)DC AB ­内错角相等,两直线平行

三、1.:∵AC平分∠DAB,

∴∠1=∠CAB,

又∵∠1=∠2,

∴∠CAB=∠2,

AB∥CD.

  1. :∵EG⊥AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> ,∠E=30°,

∴∠AKF=∠EKG=60°=∠CHF,

AB∥CD.

四、解:平行.

∵∠1=∠2,

a∥b,

又∵∠3+∠4=180°,

b∥ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> c,

a∥c.

五、∠1=∠6,∠2= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/74/" title="平行线" class="c1" target="_blank">平行线</a> <a href="/tags/245/" title="训练" class="c1" target="_blank">训练</a> <a href="/tags/847/" title="相交" class="c1" target="_blank">相交</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> ∠5,∠3=∠8,∠4=∠7,∠3=∠6,∠4=∠5,∠3+∠5=180°,∠­4+∠6=180°

六、A.