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【325169】河北省2024八年级数学上册 第12章 全等三角形 12.2 三角形全等的判定12.2

时间:2025-01-15 22:08:23 作者: 字数:2728字
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第十二章 全等三角形

12.2 三角形全等的判定

1课时 用“SSS”判定三角形全等

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1.全等三角形的三条边____________、三个角____________

2.如图,△ABC≌△BADACBD,则图中的对应边为________________________________________________________________________,对应角为________________________________

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1.三边________的两个三角形全等.可简记为“边边边”或“________”

2[2024唐山期末]如图,在纸板上先任意画一个△ABC,再画一个△DEF,使DEABDFACEFBC,将△DEF剪下来,放到△ABC上,它们完全重合吗?(  )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A.重合 B.不重合 C.不一定重合 D.无法判断

3[2023沧州月考]如图,已知ABDCACDB.求证:△ABC≌△DCB.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>





4[2024常州期中]已知:如图,点CAB的中点,CDBEADCE.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

(1)求证:△ADC≌△CEB

(2)求证:CDBE.





 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

知识点1  全等三角形的判定(SSS)

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> [2023云南中考]如图,CBD的中点,ABEDACEC.

求证:△ABC≌△EDC.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>



               


变式1如图,在△ABC和△DEF中,AB3BC4AC6DE3EF4,要使△ABC≌△DEF,则DF的长为(  )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. 3  B. 4  C. 6 D. 13




                                    

知识点2 用尺规作一个角等于已知角

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 如图,用尺规作出了∠NCB=∠AOC,作图痕迹中弧FG(  )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A.以点C为圆心,OD为半径的弧

B.以点C为圆心,DM为半径的弧

C.以点E为圆心,OD为半径的弧

D.以点E为圆心,DM为半径的弧


               


变式2[2024亳州期末]如图,已知∠BAD,用直尺和圆规在射线AD的右侧作∠DCP,使得∠DCP=∠BAD.(不写作法,只需保留作图痕迹)

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>



第十二章 全等三角形

12.2 三角形全等的判定

1课时 用“SSS”判定三角形全等

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1.分别相等;分别相等

2ACBDBCADABBA;∠CAB 和∠DBA,∠C 和∠D,∠ABC 和∠BAD

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1.分别相等;SSS 2.A

3.证明:在△ABC与△DCB中,∵

∴△ABC≌△DCB(SSS)

4.证明:(1)∵CAB的中点,

ACCB.

在△ADC和△CEB中,∵

∴△ADC≌△CEB(SSS)

(2)∵△ADC≌△CEB

∴∠ACD=∠B,∴CDBE.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1 证明:∵CBD的中点,∴BCDC.

在△ABC和△EDC中,∵

∴△ABC≌△EDC(SSS)

变式1.C 例2 D

变式2.解:如图所示.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/553/" title="河北" class="c1" target="_blank">河北</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/893/" title="河北省" class="c1" target="_blank">河北省</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>