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![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AECK có
AK//CE
AK=CE
Do đó: AECK là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AECK có
AK//CE
AK=CE
Do đó: AECK là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AECK có
AK//EC
AK=EC
Do đó: AECK là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AECK có
AK//CE
AK=CE
=>AECK là hình bình hành
b: ABCD là hình bình hành
=>AC cắt BD tại trung điểm của mỗi đường
=>O là trung điểm của AC
AECK là hbh
=>AC cắt EK tại trung điểm của mỗi đường
=>E,O,K thẳng hàng
c: Xét ΔDMC có
E là trung điểm của DC
EN//MC
=>N là trung điểm của DM
=>DN=NM
Xét ΔABN có
K là trung điểm của BA
KM//AN
=>M là trung điểm của BN
=>MB=MN=DN
![](https://rs.olm.vn/images/avt/0.png?1311)
a ) AK = 1/2 AB
CI = 1/2 CD
Mà AB //= CD nên AK //= CI suy ra
AKCI - hình bình hành
Nên AI // CK
b ) Xét t/g DNC có :
I là trung điểm CD mà IM // NC
=> IM là đường trung bình của t/g DNC
=> MD = MN ( 1 )
Xét t/g ABM có :
K là trung điểm AB mà KN // AM
=> KN là đường trung bình của t/g ABM ( 2 )
Từ ( 1 ) ; ( 2 ) suy ra DM = MN = NB
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có: \(AB=DC,AB//CD\)(ABCD là hình bình hành)
Mà \(K,E\in AB,CD;AK=\dfrac{1}{2}AB;CE=\dfrac{1}{2}CD\)
\(\Rightarrow AK=CE\) và \(AK//CE\)
=> AECK là hình bình hành
b) Ta có: O là giao điểm 2 đường chéo AC và BD
=> O là trung điểm AC
=> O là trung điểm KE(AECK là hình bình hành)
=> E,O,K thẳng hàng
Lời giải:
a. $I\in AD, K\in CB$ mà $AD\parallel CB$ (tính chất hình bình hành)
$\Rightarrow AI\parallel CK$
b.
Do $E$ là trung điểm $AB$ nên $AE=\frac{1}{2}AB$
Do $F$ là trung điểm $CD$ nên $CF=\frac{1}{2}CD$
Mà $AB=CD$ (tính chất hbh)
$\Rightarrow AE=CF$
c.
Tính chất hbh phát biểu rằng 2 đường chéo cắt nhau tại trugn điểm mỗi đường
Do đó $AC$ cắt $BD$ tại trung điểm $BD$. Mà trung điểm của $BD$ là $O$ nên $A,O,C$ thẳng hàng
Hình vẽ:
![](data:image/png;base64,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)