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TA có: \(\hat{BAG}=\hat{BAC}+\hat{GAC}=\hat{BAC}+90^0\)
\(\hat{EAC}=\hat{EAB}+\hat{BAC}=90^0+\hat{BAC}\)
Do đó: \(\hat{BAG}=\hat{EAC}\)
Xét ΔBAG và ΔEAC có
BA=EA
\(\hat{BAG}=\hat{EAC}\)
AG=AC
Do đó: ΔBAG=ΔEAC
=>BG=EC
Gọi O là giao điểm của BG và EC
ΔBAG=ΔEAC
=>\(\hat{ABG}=\hat{AEC}\)
Xét tứ giác AEBO có \(\hat{AEO}=\hat{ABO}\)
nên AEBO là tứ giác nội tiếp
=>\(\hat{BOE}=\hat{BAE}=90^0\)
=>BG⊥EC tại O
Q là tâm của hình vuông ABDE
=>Q là trung điểm chung của AD và BE
N là tâm của hình vuông ACFG
=>N là trung điểm chung của AF và CG
Xét ΔEBC có
Q,M lần lượt là trung điểm của BE,BC
=>QM là đường trung bình của ΔEBC
=>QM//EC và \(QM=\frac{EC}{2}\)
Xét ΔGEC có
P,N lần lượt là trung điêm của GE,GC
=>PN là đường trung bình cua ΔGEC
=>PN//EC và \(PN=\frac{EC}{2}\)
QM//EC
PN//EC
Do đó: QM//PN
\(QM=\frac{EC}{2}\)
\(PN=\frac{EC}{2}\)
Do đó: QM=PN
Xét ΔEBG có
Q,P lần lượt là trung điểm của EB,EG
=>QP là đường trung bình của ΔEBG
=>QP//BG và \(QP=\frac{BG}{2}\)
\(QP=\frac{BG}{2}\)
\(QM=\frac{EC}{2}\)
mà BG=EC
nên QP=QM
QP//BG
BG⊥EC
Do đó: QP⊥EC
QP⊥EC
EC//QM
Do đó: QP⊥QM
Xét tứ giác MNPQ có
MQ//NP
MQ=NP
Do đó: MNPQ là hình bình hành
Hình bình hành MNPQ có QM⊥QP
nên MNPQ là hình chữ nhật
Hình chữ nhật MNPQ có QM=QP
nên MNPQ là hình vuông
bạn tự vẽ hình nhé
CM tam giác ABC= tam giác AEG
\(\Rightarrow\)góc GEA= góc ABC
góc EGA = góc ACB
ta có góc HAC= góc ABH ( cùng phụ goc BAH)
góc OAE= góc HAC
\(\Rightarrow\) góc OEA= góc OAE
\(\Rightarrow\)OA=OE
CMTT: OA=OG
suy ra OE=OG (1)
ta có góc GAC+ HAC+BAH=180độ
mà BAH=OAG
 \(\Rightarrow\) OAG+GAC+HAC=180 độ
O,A ,H thẳng hàng(2)
từ 1 va 2 suy ra đfcm
O là trung điểm EG
Tứ giác EGCD có :
góc EBC = góc GCB = góc EGC = 90 độ
-> EGCB là hình chữ nhật
Mà P,Q,M,N lần lượt là đỉnh của 4 cạnh
->MNPQ là hình vuông
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
đề có sai ko vậy bn ,mk thấy phải cho tam giác cân chứ , mk vẽ thử r
nhọn nha bạn
đề đúng mà Giang
ukm , bn