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【330096】18.1.2 平行四边形的判定(3)——判定与性质

时间:2025-02-08 16:45:26 作者: 字数:2667字

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>  <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

18.1.2 平行四边形的判定3)——判定与性质

课堂学习检测

一、填空题

1.平行四边形长边是短边的2倍,一条对角线与短边垂直,则这个平行四边形各角的度数分别为______

2.从平行四边形的一个锐角顶点作两条高线,如果这两条高线夹角为135°,则这个平行四边形的各内角的度数为______

3.在ABCD中,BC2AB,若EBC的中点,则∠AED______

4.在ABCD中,如果一边长为8cm,一条对角线为6cm,则另一条对角线x的取值范围是______

5ABCD中,对角线ACBD交于O,且ABAC2cm,若∠ABC60°,则△OAB的周长为______cm

6.如图,在ABCD中,MBC的中点,且AM9BD12AD10,则ABCD的面积是______

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

7ABCD中,对角线ACBD交于点O,若∠BOC120°AD7BD10,则ABCD的面积为______

8.如图,在ABCD中,AB6AD9,∠BAD的平分线交BC于点E,交DC的延长线于点FBGAE,垂足为GAF5 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> ,则△CEF的周长为______

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

9.如图,BDABCD的对角线,MN分别在ADAB上,且MNBD,则S△DMC______

SBNC(填“<”、“=”或“>”)

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

综合、运用、诊断

一、解答题

10.已知:如图,△EFC中,AEF边上一点,ABECADFC,若∠EAD=∠FABABaADb

(1)求证:△EFC是等腰三角形;

(2)ECFC

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>













11.已知:如图,△ABC中,∠ABC90°BDACDAE平分∠BACEFDC,交BCF.求证:BEFC

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>







12.已知:如图,在ABCD中,EAD的中点,CEBA的延长线交于点F.若BC2CD,求证:∠F=∠BCF

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>







13.如图,已知:在ABCD中,∠A60°EF分别是ABCD的中点,且AB2AD.求证:BFBD <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> 3

 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>








参考答案

160°120°60°120°245°135°45°135°

390°410cmx22cm5 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

672.提示:作DEAMBC延长线于E,作DFBEF,可得△BDE是直角三角形, <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

7 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> 提示:作CEBDE,设OEx,则BE2CE2BC2,得(x5)2 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> .解出 <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> S2SBCDBD×CE <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a>

879.=.提示:连结BMDN

10(1)提示:先证∠E=∠F(2)ECFC2a2b

11.提示:过E点作EMBC,交DCM,证△AEB≌△AEM

12.提示:先证DCAF

13.提示:连接DE,先证△ADE是等边三角形,进而证明∠ADB90°,∠ABD30°