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【330170】19.2特殊的平行四边形课时练

时间:2025-02-08 16:51:15 作者: 字数:10528字

19.2特殊的平行四边形课时练

课时一矩形

1.矩形具有而平行四边形不具有的性质是(

A.对边相等 B.对角相等 C.对角互补 D.对角线平分

2.直角三角形中,两直角边长分别为125,则斜边中线长是(

A.26 B.13 C.8.5 D.6.5

3组合 7 .矩形ABCD对角线ACBD交于点OAB=5 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 则△ABO的周长为等于

.

4. 如图所示,四边形ABCD为矩形纸片.把纸片ABCD折叠,

使点B恰好落在CD边的中点E处,折痕为AF.若CD6

AF等于 (  )

A组合 25 . <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>   B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>    C. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> D.8  

5. 如图所示,矩形 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 的对角线 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 相交于点 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

过点 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 的直线分别交 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 于点EF <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

则图中阴影部分的面积为     

6.已知矩形的周长为40 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,被两条对角线分成的相邻两个三角形的周长

的差为8 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则较大的边长为 .

7. 如图,矩形ABCD中,ACBD交于O点, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> E <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> F

组合 42 求证BE=CF







8组合 45 . 如图所示,EABCD外,AE⊥CE,BE⊥DE

求证:ABCD为矩形






9.已知矩形ABCD和点P,当点P在图1中的位置时,则有结论:SPBC=SPAC+SPCD理由:过点PEF垂直BC,分别交ADBCEF两点.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

l

S△PBC+S△PAD=BC·PF+AD·PE=BCPF+PE=BC·EF=S矩形ABCD

又∵ SPAC+SPCD+SPAD=S矩形ABCD

S△PBC+S△PAD= SPAC+SPCD+SPAD

S△PBC=S△PAC+S△PCD

请你参考上述信息,当点P分别在图2、图3中的位置时,S△PBCSPACSPCD又有怎样的数量关系?请写出你对上述两种情况的猜想,并选择其中一种情况的猜想给予证明.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

2 3


1 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 0. 如图所示,△ABC中,点OAC边上一个动点,过点O作直线MNBC,设MN交∠BCA的平分线于E,交∠BCA的外角平分线于点F.

(1)求证:EO=FO

(2)当点O运动到何处时,四边形AECF是矩形?并证明你的结论.



10题图




课时一答案:

1.C2.D,提示:由勾股定理求得斜边为: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,斜边的中线长为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>3.18,提示:AB=5,BC=12,AC=13, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 4. A,提示:DE=3,AB=AE=6,在直角三角形ADE中,∠DAE=30 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,由折叠的性质得∠BAF=EAF=30,BF= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则AF=2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>5.36.14

7证明:∵四边形ABCD为矩形,AC=BD,BO=CO,

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> , <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,BEO=CFO=90 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,又∵∠BOE=COF

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ∴BE=CF

8 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> .连接ACBDACBD相交于点O,连接OE

ABCD中,AO=OC,BO=DO.  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 中,OE= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 中,OE= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴BD=AC, ∴ABCD为矩形.

9. 猜想结果:图2结论SPBC=SPAC+SPCD; 图3结论SPBC=SPAC-SPCD

证明:如图2,过点PEF垂直AD,分别交ADBCEF两点.

S△PBC=BC·PF=BC·PE+BC·EF

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

=AD·PE+BC·EF=S△PAD+S矩形ABCD

SPAC+S△PCD=SPAD+SADC=SPAD+S矩形ABCD

SPBC=SPAC+S△PCD

10. (1)证明:∵MNBC,∴∠BCE=CEO又∵∠BCE=ECO

∴∠OEC=OCEOE=OC,同理OC=OF,∴OE=OF

(2)OAC中点时,AECF为矩形,∵EO=OF(已证)OA=OC

AECF为平行四边形,又∵CECF为△ABC内外角的平分线

∴∠EOF=90°,∴四边形AECF为矩形

组合 51 时二菱形

1. 如图,在菱形ABCD中,对角线ACBD相交于点OEBC

中点,则下列式子中一定成立的是(   )

A组合 54 AC=2OE BBC=2OE

CAD=OE DOB=OE

2组合 65 . 如图,在菱形ABCD中,不一定成立的(  )

A.四边形ABCD是平行四边形

B.ACBD

C.ABD是等边三角形

D.CAB=∠CAD

3. 如图,如果要使 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 成为一个菱形,

需要添加一个条件,那么你添加的条件是

4. 菱形的两条对角线长分别是68,则菱形的边长为

5.ABCD的对角线相交于点O,分别添加下列条件:①ACBD;②AB=BC;AC平分∠BAD;④AO=DO,使得ABCD是菱形的条件有(

A.1 B.2 C.3 D.4

6.菱形的周长为20 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,一条对角线长为8 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则菱形的面积为 .

7. 在四边形ABCD中,对角线ACBD交于点O,从(1)AB=CD(2)ABCD(3)OA=OC(4)OB=OD(5)ACBD(6)AC平分∠BAD这六个条件中,选取三个推出四边形ABCD是菱形。如(1)(2)(5) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ABCD是菱形,再写出符合要求的两个:________ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ABCD是菱形;________ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ABCD是菱形。

8组合 77 . 如图所示,AD是△ABC的角平分线.DEACABEDFABACF.四边形AEDF是菱形吗?说明你的理由.








9..ABCD的对角线AC的垂直平分线与边ADBC分别交于EF,四边形AFCE是否是菱形?为什么?

组合 80







10.. 已知:如图,在ABCD 中,EF分别为边ABCD的中点,BD是对角线,AGDBCB的延长线于G

1)求证:△ADE≌△CBF

2)若四边形 BEDF是菱形,则四边形AGBD是什么特殊四边形?并证明你的结论.

组合 74









课时二答案:

1. B2. C; 3.答案不唯一: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 等;4.55.C6.24,提示:由已知得菱形一边长为5 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,由菱形的对角线互相平分且垂直,所以另一条对角线的长为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴S= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 7.①②⑥或③④⑤或③④⑥;

8.四边形AEDF是菱形,∵DEAC∴∠ADE=∠DAF

AD是△ABC的角平分线,

∴∠DAE=∠DAF,∴∠ADE=DAE,∴AE=ED.

又∵DEACDFAB

四边形AEDF是平行四边形,∴平行四边形AEDF是菱形.

9. AFCE是菱形,△AOE≌△COF,四边形AFCE是平行四边形,EFAC


10.. 解:(1)∵四边形ABCD是平行四边形,∴∠1=∠CADCBABCD

E F分别是ABCD的中点,∴AE <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> AB CF <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> CD

∴AECF .∴△ADE≌△CBF

2)当四边形BEDF是菱形时,四边形 AGBD是矩形.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 四边形ABCD是平行四边形,∴ADBC

∵AGBD ,∴四边形 AGBD 是平行四边形.

四边形 BEDF 是菱形,

∴DEBE .∵AEBE

∴AEBEDE

∴∠1=∠2,∠3=∠4

∵∠1+∠2+∠3+∠4180°,∴2223180°

∴∠2+∠390°

即∠ADB90°

四边形AGBD是矩形.

课时三正方形

1. 四边形ABCD中,ACBD相交于点O,能判别这个四边形是正方形的条件是(

A.OA=OB=OC=ODACBD B.ABCDAC=BD

C.ADBC,∠A=C D.OA=OCOB=ODAB=BC

2. 在正方形ABCD中,AB=12 cm,对角线ACBD相交于O,则△ABO的周长是(

A.12+12 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> B.12+6 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> C.12+ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> D.24+6 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

3. 已知四边形ABCD是菱形,当满足条件_________时,它成为正方形(填上你认为正确的一个条件即可).

4. 下列命题中的假命题是( )

A.一组邻边相等的平行四边形是菱形

B.一组邻边相等的矩形是正方形

c 一组对边平行且相等的四边形是平行四边形

D.一组对边相等且有一个角是直角的四边形是矩形

5. 正方形的一条边长是3,那么它的对角线长是_______.

6. 如图,依次连结一个边长为1的正方形各边的中点,得到第二个正方形,再依次连结第二个正方形各边的中点,得到第三个正方形,按此方法继续下去, 则第六个正方形的面积是

组合 83

画布 86





7组合 97 . 如图,四边形ABCD为正方形,ADE为等边三角形,AC为正方形ABCD的对角线,则∠EAC___度.

8. 已知如下图,正方形ABCD中,ECD边上的一点,

FBC延长线上一点,CE=CF.

(1)求证:△BEC≌△DFC

(2)若∠BEC=60°,求∠EFD的度数.

9组合 141 如图所示,.四边形ABCDDEFG都是正方形,连接AECG

1求证:AE=CG

2观察图形,猜想AECG之间的位置关系,

并证明你的猜想.



1组合 100 0. 把正方形 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 绕着点 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,按顺时针方向旋转得到正方形 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,边 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 交于点 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> (如图).试问线段 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 与线段 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 相等吗?

请先观察猜想,然后再证明你的猜想.









11.如图,点E在正方形ABCD的边CD上运动,ACBE交于点F

1)如图1,当点E运动到DC的中点时,求△ABF与四边形ADEF的面积之比;

2)如图2,当点E运动到CEED=21时,求△ABF与四边形ADEF的面积之比.

3)当点E运动到CEED=31时,写出△ABF与四边形ADEF的面积之比;当点E运动到CEED=n1n是正整数)时,猜想△ABF与四边形ADEF的面积之比(只写结果,不要求写出计算过程);

4)请你利用上述图形,提出一个类似的问题(根据提出的问题给附加分,最多4分,计入总分,但总分不超过120分).

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>


课时三答案:

1.A2.A; 3.A=90°或∠B=90°或∠C=90°或∠D=90°中的任一条件即可;4. D5. 3 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

6.  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ;7.105;

8.证明:(1)四边形ABCD是正方形.BC=DC,∠BCD=90°

RtBCERtDCF中,BC=DCCE=CF,RtBCERtDCF

(2)CE=CF,∴∠CEF=CFE,∴∠CFE= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> (180°90°)=45°

RtBCERtDCF,∴∠CFD=BEC=60°

∴∠EFD=DFC-∠EFC=15°

9. (1) 证明: 如图,∵ AD=CDDE=DG,∠ADC=∠GDE=90o

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> CDG=90o +∠ADG=∠ADE

∴ △ADE≌△CDG AE=CG

2猜想: AECG

证明: 如图,

AECG交点为MADCG交点为N

∵ △ADE≌△CDG DAE=∠DCG  

又∵ ANM=∠CND AMN∽△CDN

∴ ∠AMN=∠ADC=90o.∴ AECG


10. 组合 126 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

证法1:连结 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 四边形 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 都是正方形.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

由题意知 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ,又 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 组合 112

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

证法2:连结 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 四边形 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> 都是正方形,

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

由题意知 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>


11. 解:(1)如图1,连结DF

因为点ECD的中点,所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

据题意可证△FEC∽△FBA,所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> . (2分)

因为SDEF=SCEFS=S 2分)

所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

2)如图2,连结DF

与(1)同理可知, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> = <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> SDEF= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> SCEF <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> = <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

3)当CEED=31时,= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a>

CEED=n1时, = <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> = <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/915/" title="特殊" class="c1" target="_blank">特殊</a> ).

4)提问举例:①当点E运动到CEED=51时,△ABF与四边形ADEF的面积之比是多少?

当点E运动到CEED=23时,△ABF与四边形ADEF的面积之比是多少?

当点E运动到CEED=mnmn是正整数)时,△ABF与四边形ADEF的面积之比是多少?