内容正文:
书书书
!"#$
1.
!"
1,
#$%
ABCD
&
,AB=4,∠BAD=120°,
△AEF'()*+%,E,F#$%,)BC,CD-.
(1)
./
:BE=CF;
(2)
01
E,F
23#)
BC,CD
-456
(△AEF!
"#$%&'(
),
789:)%
AECF
,;<=>?
@AB
?
CDA
,
EFGHIJ
;
CAB
,
7K/LM
.
2.
%&'()
#NOP%QR
ABCD
&
,AB =25cm,AD =
20cm,
STGOQRUVW"XYZ[\
.
(1)
!"
2①,[]'DE,1A,^_1F#CD-,
`[]
DE
,a=
cm;
(2)
!"
2②,H,G23'BC,AD,&1,A,^_
1
F
#
HG
-
,
[]'
DE,
Ebcd2,;<
;
(3)
!"
2③,T"2②&,aY%ABCDefHG
gh
,
AijOaY%QR
,
TjOQRklm
,
o
pm\:)%,%q
,
r./
.
书书书
!
、
"#$%&'(
)
1
!"
1,
#$%
ABCD
&
,BC=8,CD=4,
'△BCD()
*+
BD
,-
,
.
C
/#.
C′
0
,
BC′
1
AD
2.
E,
3+4
DE
56
7
( )
A.3 B.154 C.5 D.
15
2
*+
:
89:;<=>?
BE=DE,
@A:;BCD
E>?+4
AB,AE,BE
5FG
,
HFGIJ
.
,
:
K
ED=x,
3
AE=8-x.
L7MN%
ABCD
7$%
,
OP
AD∥BC.
OP∠EDB=∠DBC.
L7-Q
,
OP∠EBD=∠DBC.
OP∠EDB=∠EBD.OPEB=ED=x.
#
Rt△ABE&,RBCDE,>BE2 =AB2+AE2,
I
x2 =42+(8-x)2,
H>
x=5.
OP
ED=5.
ST
C.
-
、
"#$%&./0
)
2
!"
2,
#$%
ABCD
&
,AB=4,AD=6,E
U
AB
N5
&.
,F
U+4
BC
NV5W.
,
'△EBF(EFO#X+-Q>
?△EB′F,YZ B′D,3 B′D5
[\]U
.
*+
:
YZ
ED
A^_△DEB′&`NaD,bcDB′5
6d[\
,
ef.
B′
/#
DE
V
,
ef
DB′=DE-EB′.
,
:
!"
3,
L7
E
U
AB
N
5&.
,AB=4,
OP
AE=EB
= 12AB=2.
L7MN%U
ABCD
$%
,
OP∠A=90°.
L7
AD=6,
OP
ED= 62+2槡
2 =2槡10.
:;,-)g5hiJj
EB′=EB=2.
L7△DEB′&`NaD,bcDB′56d[\,e
f.
B′
/#
DE
V
.
OP
DB′=DE-EB′=2槡10-2.
OP
DB′
6d5[\]7
2槡10-2.
1
、
"#$%23456
)
3
!"
4,
'$%
ABCD
(
DE
-Q
,
ck.
A
/#
DC
V
5.
A′
0
,
@A'$%lm
,
(
EF
-Q
,
ck.
A
/#-n
DE
V5.
G
0
.
o'$%
ABCD
(
CE
-Q
,
efk.
B
pq/#
DE
V5.
H
0
.
(1)
rs
:EG=CH;
(2)
tj
AF=槡2,rADuAB56.
*+
:(1)
R-Q5hiv$%5hiJj
AE=
AD=EG,BC=CH,
o:;MN%
ABCD
U$%
,
J>
AD=BC,
wxyzIJs{
EG=CH;
(2)
R-Q5hiJj∠ADE=45°,∠FGE=∠A
=90°,AF=槡2,|}DG=槡2,~�BCDEr�DF
=2,
J>
AD=AF+DF=槡2+2;os{ △AEF≌
△BCE,>?AF=BE,2U>?AB56.
,
:(1)
s{
:
R-Qj
AE=AD=EG,BC=CH,
L7MN%
ABCD
U$%
,
OP
AD=BC.
OP
EG=CH.
(2)
L7∠ADE=45°,∠FGE=∠A=90°,AF=
槡2,OPDG=槡2,DF=2.
OP
AD=AF+DF=槡2+2.
R-Qj∠AEF=∠GEF,∠BEC=∠HEC,
OP∠GEF+∠HEC=90°,∠AEF+∠BEC=90°.
L7∠AEF+∠AFE=90°,OP∠BEC=∠AFE.
#△AEF�△BCE&,
∠AFE=∠BEC
∠A=∠B=90°,{
AE=BC
OP△AEF≌△BCE(AAS).OPAF=BE.
OP
AB=AE+BE=槡2+2+槡2=2槡2+2.
书书