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![](https://rs.olm.vn/images/avt/0.png?1311)
a) Xét tứ giác AMCK:
I là trung điểm của AC (gt).
I là trung điểm của MK (K là điểm đối xứng với M qua I).
Mà \(\widehat{AMC}=90^o\left(AM\perp BC\right).\)
=> Tứ giác AMCK là hình chữ nhật (dhnb).
b) Xét tam giác ABC cân tại A: AM là đường cao (gt).
=> AM là trung tuyến (Tính chất tam giác cân).
=> M là trung điểm của BC.
=> BM = MC.
Ta có: AK = MC (Tứ giác AMCK là hình chữ nhật).
BM = MC (cmt).
=> AK = MC = BM.
Ta có: AK // MC (Tứ giác AMCK là hình chữ nhật).
=> AK // BM.
Xét tứ giác AKMB:
AK // BM (cmt).
AK /= BM (cmt).
=> Tứ giác AKMB là hình bình hành (dhnb).
c) Tứ giác AMCK là hình vuông (gt).
=> AK = AM (Tính chất hình vuông).
Mà AK = BM (cmt).
=> AM = BM = AK.
Mà BM = \(\dfrac{1}{2}\) BC (M là trung điểm BC).
=> AM = BM = AK = \(\dfrac{1}{2}\) BC.
Xét tam giác ABC cân tại A:
AM = \(\dfrac{1}{2}\) BC (cmt).
=> Tam giác ABC vuông cân tại A.
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AMBN có
I là trung điểm chung của AB và MN
góc AMB=90 độ
Do đó: AMBN là hình chữ nhật
b: Xét tứ giác ACMN có
AN//CM
AN=CM
Do đó: ACMN là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AMCK có
I là trung điểm chung của AC và MK
góc AMC=90 độ
Do đó: AMCKlà hình chữ nhật
b: Xét tứ giác AKMB có
AK//MB
AK=MB
Do đó: AKMB là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác ANMC có
MN//AC
MN=AC
Do đó: ANMC là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AMCK có
I là trung điểm chung của AC và MK
góc AMC=90 độ
Do đo: AMCK là hình chữ nhật
b: Xét tứ giác AKMB có
AK//MB
AK=MB
Do đó: AKMB là hình bình hành
=>AB=MK
c: Để AMCK là hìh vuông thì AM=CM=BC/2
=>ΔABC vuông tại A
d: P=(5+5+6)/2=8
\(S=\sqrt{8\left(8-6\right)\left(8-5\right)\left(8-5\right)}=\sqrt{16\cdot9}=12\left(cm^2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)AMBN có: AI=IB; NI=IM
=> AM BN là hbh (1).
ABC có AM là đttuyen
=> AM là đcao
=> AM vuông góc với BC (2).
Từ 1 2 => AMBN là hcn.
b)AMBN là hcn => AN=BM và AN song song với BM mà BM=MC và B, M, C thẳng hàng => AN=MC và AN song song với MC => ACMN là hbh.
c) ABC là tam giác vuông cân
Lời giải:
a. $M,N$ đối xứng nhau qua $O$ nghĩa là $O$ là trung điểm $MN$
Tứ giác $AMBN$ có 2 đường chéo $AB, MN$ cắt nhau tại trung điểm $O$ của mỗi đường nên $AMBN$ là hbh $(1)$
Mặt khác, tam giác $ABC$ cân tại $A$ nên trung tuyến $AM$ đồng thời là đường cao
$\Rightarrow AM\perp BC$ nên $\widehat{AMB}=90^0(2)$
Từ $(1); (2)\Rightarrow AMBN$ là hình chữ nhật
b. Vì $AMBN$ là hcn nên $BM\parallel AN$ và $BM=AN$
Mà $B,M,C$ thẳng hàng và $BM=MC$ nên:
$AN\parallel CM, AN=CM$
$\Rightarrow ACMN$ là hình bình hành
c.
$ACMN$ là hbh nên $MN\parallel AC$
Để $ACMN$ là hình vuông thì $MN\perp AB$
$\Leftrightarrow AC\perp AB$
$\Leftrightarrow ABC$ là tam giác vuông tại $A$
Hình vẽ:
![](data:image/png;base64,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)