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![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác ABEC có
D là trung điểm của BC
D là trung điểm của AE
Do đó: ABEC là hình bình hành
mà \(\widehat{BAC}=90^0\)
nên ABEC là hình chữ nhật
b: Xét ΔBAG có
BH là đường cao
BH là đường trung tuyến
Do đó: ΔBAG cân tại B
Suy ra: BA=BG
mà BA=CE
nên BG=CE
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Xét tứ giác ABEC có
M là trung điểm của đường chéo BC(gt)
M là trung điểm của đường chéo AE(A và E đối xứng nhau qua M)
Do đó: ABEC là hình bình hành(Dấu hiệu nhận biết hình bình hành)
Hình bình hành ABEC có \(\widehat{CAB}=90^0\)(ΔABC vuông tại A)
nên ABEC là hình chữ nhật(Dấu hiệu nhận biết hình chữ nhật)
b) Vì D đối xứng với M qua AB(gt)
nên AB là đường trung trực của DM
⇔AB vuông góc với DM tại trung điểm của DM
mà AB cắt DM tại H(gt)
nên H là trung điểm của DM và MH⊥AB tại H
Ta có: MH⊥AB(cmt)
AC⊥AB(ΔABC vuông tại A)
Do đó: MH//AC(Định lí 1 từ vuông góc tới song song)
hay MD//AC
Ta có: H là trung điểm của MD(cmt)
nên \(MH=\dfrac{1}{2}\cdot MD\)(1)
Xét ΔABC có
M là trung điểm của BC(gt)
MH//AC(cmt)
Do đó: H là trung điểm của AB(Định lí 1 đường trung bình của tam giác)
Xét ΔABC có
M là trung điểm của BC(gt)
H là trung điểm của AB(cmt)
Do đó: MH là đường trung bình của ΔABC(Định nghĩa đường trung bình của tam giác)
⇒\(MH=\dfrac{1}{2}\cdot AC\)(Định lí 2 đường trung bình của tam giác)(2)
Từ (1) và (2) suy ra AC=MD
Xét tứ giác ACMD có
AC//MD(cmt)
AC=MD(cmt)
Do đó: ACMD là hình bình hành(Dấu hiệu nhận biết hình bình hành)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)Ta có
BK=KC (GT)
AK=KD( Đối xứng)
suy ra tứ giác ABDC là hình bình hành (1)
mà góc A = 90 độ (2)
từ 1 và 2 suy ra tứ giác ABDC là hình chữ nhật
b) ta có
BI=IA
EI=IK
suy ra tứ giác AKBE là hình bình hành (1)
ta lại có
BC=AD ( tứ giác ABDC là hình chữ nhật)
mà BK=KC
AK=KD
suy ra BK=AK (2)
Từ 1 và 2 suy ra tứ giác AKBE là hình thoi
c) ta có
BI=IA
BK=KC
suy ra IK là đường trung bình
suy ra IK//AC
IK=1/2AC
mà IK=1/2EK
Suy ra EK//AC
EK=AC
Suy ra tứ giác AKBE là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AEBF có
D là trung điểm của AB
D là trung điểm của EF
Do đó: AEBF là hình bình hành
b: Xét tứ giác ABFO có
AO//BF
AO=BF
Do đó: ABFO là hình bình hành
mà \(\widehat{BAO}=90^0\)
nên ABFO là hình chữ nhật
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
b. Ta thấy: $5^2+12^2=13^2$ hay $AB^2+AC^2=BC^2$ nên tam giác $ABC$ vuông tại $A$.
Tứ giác $ACEB$ có 2 đường chéo $BC,AE$ cắt nhau tại trung điểm $D$ của mỗi đường nên là hình bình hành.
Mà $\widehat{A}=90^0$ nên $ACEB$ là hình chữ nhật.
a.
$ACEB$ là hcn nên $AE=BC=13$ (cm)
$\Rightarrow AD=AE:2=13:2=6,5$ (cm)
c.
Để $ABEC$ là hình vuông thì $AB=AC$. Khi đó $ABC$ phải là tam giác vuông cân tại A chứ không liên quan gì đến điểm D hết bạn nhé.
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
Ta có: MB = MC; MA = MD (gt)
⇒ Tứ giác ABDC là hình bình hành
Mà: ∠A = 90°
⇒ Tứ giác ABDC là hình chữ nhật (đpcm)
b)
Gọi O là giao điểm của AC và AE
ΔAED có: OA = OE (E đối xứng với A qua BC); MA = MD (gt)
⇒ OM là đường trung bình của ΔAED
⇒ OM // ED (1)
Vì: E đối xứng với A qua BC
⇒ BC là đường trung trực của AE
⇒ BC ⊥ AE hay OM ⊥ AE (2)
Từ (1), (2) ⇒ ED ⊥ AE (đpcm)
c)
Ta có: BC // ED (OM // ED)
⇒ Tứ giác BEDC là hình thang
Ta có: BD = AC (Tứ giác ABDC là hình chữ nhật) (a)
ΔAEC có: CO vừa là đường trung tuyến vừa là đường cao
⇒ ΔAEC cân tại C ⇒ CA = CE (b)
Từ (a), (b) ⇒ BD = EC
Hình thang BEDC có: BD = EC
⇒ Tứ giác BEDC là hình thang cân
Lời giải:
a. $M$ là trung điểm $BC$, $N$ là trung điểm $AC$ thì $MN$ là đường trung bình của tam giác $ABC$ ứng với cạnh $AB$
$\Rightarrow MN=\frac{1}{2}AB=\frac{1}{2}.12=6$ (cm)
b. $E, A$ đối xứng nhau qua $M$ nghĩa là $M$ là trung điểm $AE$.
Tứ giác $ABEC$ có 2 đường chéo $BC, AE$ cắt nhau tại trung điểm $M$ của mỗi đường nên $ABEC$ là hình bình hành
Mà $\widehat{BAC}=90^0$ nên $ABEC$ là hình chữ nhật.
b. Vì $B,D$ đối xứng nhau qua $A$ nên $BA=AD$
$ABEC$ là hcn (cmt) nên $AB=EC$
$\Rightarrow AD=EC$ (đpcm)
Mặt khác:
$ABEC$ là hcn nên $AB\parallel EC\Rightarrow AD\parallel EC$
Xét tứ giác $ADCE$ có $AD=CE$ và $AD\parallel CE$ nên $ADCE$ là hbh (đpcm)
Hình vẽ:
![](data:image/png;base64,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)