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,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Company name,*,Click to edit Master title style,LOGO,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Company name,*,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,Company name,*,单击此处编辑母版标题样式,LOGO,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,单击此处编辑母版标题样式,18,.2,特殊的平行四边形,第18章 平行四边形,第,1,课时 菱形的性质,18,.2.2,菱形,活动1,平行四边形与菱形,平行四边形,一组邻边相等,菱形,菱形的定义:,活动,2,有一组邻边相等的平行四边形叫做菱形,.,请欣赏:,你还能举出一些例子吗?,活动,2,思考:因为菱形是平行四边形,所以它具有平行四边形的所有性质,.,由于它的一组邻边相等,它是否具有一般平行四边形不具有的一些特殊性质呢?,活动,3,菱形具有一般平行四边形不具有的一些特殊性质,.,菱形的性质,1.,将一张矩形的纸对折再对折,沿对折的部分剪下一直角三角形,打开,你发现这是一个什么样的图形?,活动,3,2.,菱形是不是轴对称图形?如果是,它有几条对称轴?,菱形,是轴对称图形,有两条对称轴,.,3.,菱形除了具有平行四边形的性质以外,它还有什么特殊性质呢?它的边、对角线之间有什么关系?,活动,3,4.,你能证明上述结论吗?,菱形的四条边都相等;,菱形的两条对角线互相垂直,并且每一条对角线平分一组对角,.,活动,3,菱形的四条边都相等,.,已知:如图,四边形,ABCD,是菱形,.,求证:,AB,=,BC,=,CD,=,DA,.,证明: 四边形,ABCD,是菱形,, 四边形,ABCD,是平行四边形,且,AB,=,BC,.,AB,=,CD,,,BC,=,DA,.,AB,=,BC=CD,=,DA,.,D,C,B,A,活动,3,菱形的两条对角线互相垂直,并且每一条对角线平分一组对角,.,证明: 四边形,ABCD,是菱形,, 四边形,ABCD,是平行四边形,,且,AB,=,BC,=,CD,=,DA,.,AO,=,CO,,,BO,=,DO,.,AC,BD,,,且,ABO,=,CBO,,,ADO,=,CDO,,,BAO,=,DAO,,,BCO,=,DCO,.,AC,平分,BAD,和,BCD,,,BD,平分,ABC,和,ADC,.,O,D,C,B,A,已知:如图,四边形,ABCD,是菱形,,对角线,AC,,,BD,交于点,O,.,求证:,AC,BD,;,AC,平分,BAD,和,BCD,,,BD,平分,ABC,和,ADC,.,思考:,(,1,)怎样求菱形的面积?,(,2,)你发现菱形被对角线分成的四个小三角形有什么特点?菱形是否还有其他的求面积的方法?,活动,4,探究菱形的面积公式,面积,=,底,高,四个小三角形是全等的直角三角形,如果菱形的两条对角线长分别为,a,,,b,,,则菱形的面积,S,=,ab,.,菱形性质的应用,例 如图,菱形花坛,ABCD,的边长为,20,m,,,A,BC,=60,,沿着菱形的对角线修建了两条小路,AC,和,BD,.,求,两条小路的长(结果保留小数点后两位)和花坛的面积(结果保留小数点后一位,),.,解: 花坛,ABCD,的形状是菱形,,AC,BD,,,ABO,=,ABC,=,60=30.,在,Rt,OAB,中,,AO,=,AB,=,20=10,,,花坛的两条小路长,AC,=2,AO,=20,(,m,),,(,m,),.,花坛的面,积,(,m,2,),.,活动,5,A,B,C,D,O,活动,5,练习,1,四,边形,ABCD,是菱形,对角线,AC,,,BD,相交于点,O,,且,AB,=5,,,AO,=4.,求,AC,和,BD,的长,.,解: 四边形,ABCD,是菱形,,AC,BD,,,AO,=,CO,,,DO,=,BO,.,AB,=5,,,AO,=4,,,在,Rt,OAB,中,,BO,=,=3,,,AC,=2,AO,=8,,,BD,=2,BO,=6.,O,C,B,D,A,活动,5,练习,2,已知菱形的两条对角线的长分别是,6,和,8,,,求菱形的周长和面积,.,解: 四边形,ABCD,是菱形,,AC,BD,,,AO,=,CO,,,DO,=,BO,.,AC,=8,,,BD,=6,,,AO,=4,,,BO,=3.,在,Rt,OAB,中,,AB,=,=,5.,周长,=4,AB,=20,,,面积,=,AC,BD,=24.,O,C,B,D,A,小结:,本节课你学习了哪些内容?,你最大的收获是什么?,活动,6,教材习题,18.2,第,5,题,.,活动,6,作业:,谢谢,!,
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