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Hồ Quốc Khánh
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Trần Thị Loan
26 tháng 11 2014 lúc 16:56

A B C D F E

vì tam giác ABE đều nên góc ABE = AEB = 600

suy ra goc EBC = 90 - 30 = 600

vì tam giác BFC đều nên goc FBC = FCB = 60o

Ta có tam giác EBF cân tại B (vì BE =BF ) và goc EBF = EBC + CBF = 60+30 = 90o

suy ra goc BEF = \(\frac{180-90}{2}\)=45o

ta có goc AEF = AEB + BEF = 60 + 45 = 105o

ta có tam giac AED cân tại A(vì AD = AE) và goc EAD = 30o nên goc AED = \(\frac{180-30}{2}\)= 75o

Ta có goc AED + goc AEF = 75 + 105 = 180o

suy ra D, E, F thẳng hàng

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Nguyen ngoc linh
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Hehe boi
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undefined

Do góc DAM = góc AMB=600, mà 2 góc này slt nên AD//BC=> ABCD là hình thang

Mà góc ABC= góc DCB=600 nên ABCD là hình thang cân.

Còn O là điểm gì thì mik ko bt

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Do AM=AB, AD//BC nên ABCM là hình thoi.

Ma AC và BM là 2 đường chéo nên OAM=OAB=600/2=300.

Tương tự ta cx có OBM=OBC=600/2=300.

=> ABO=600+300=900

Do Tam giác ABO có B=900 và A=300 nên đây là tam giác nửa đều.

=>AO=2OB. (1)

Mà O là giao điểm 2 đg chéo hình thg cân nên OA=OD. (2)

Từ (1),(2), ta có OD=2OB.

(DO MÌNH TỰ GIẢI NÊN CÓ GÌ SAI BN SỬA LẠI NHA!)undefined

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Hehe boi
11 tháng 8 2021 lúc 17:34

O là giao điểm của ADC và BD bạn nhé

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Hoàng Lâm
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Trần Khánh Vân
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Thiên An
22 tháng 3 2016 lúc 16:30

A B C D E F G H

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Thiên An
22 tháng 3 2016 lúc 16:35

Giả sử tứ giác ABCD định hướng âm. Gọi \(f\) là phép quay vec tơ theo góc \(\frac{\pi}{3}\) ta có

\(\overrightarrow{EG}=\overrightarrow{AG}-\overrightarrow{AE}=\overrightarrow{AB}+\overrightarrow{BG}-\overrightarrow{AE}\)

suy ra \(f\left(\overrightarrow{EG}\right)=f\left(\overrightarrow{AB}\right)+f\left(\overrightarrow{BG}\right)-f\left(\overrightarrow{AE}\right)\)

                        \(=\overrightarrow{AE}+\overrightarrow{BC}-\overrightarrow{BE}\)

                        \(=\overrightarrow{AC}\)

Tương tự ta cũng chứng minh được \(f\left(\overrightarrow{HF}\right)=\overrightarrow{AC}\)

Từ đó suy ra \(\overrightarrow{EG}=\overrightarrow{HF}\)

Do đó tứ giác EGFH là hình bình hành

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chả pít
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dsfdsf
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Trịnh Việt Dũng
15 tháng 6 2022 lúc 20:31

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Hà Hoàng
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Nguyễn Chí Cường
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Seu Vuon
3 tháng 2 2015 lúc 10:57

Bài này khó đó bạn, có lẽ phải vẽ thêm đường phụ

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Lê Thị Quỳnh
3 tháng 2 2015 lúc 12:59

Có hai cách vẽ thêm hình phụ ở bài này:

Dựng tam giác đều IFB, I nằm trong tam giác CFB.

Hoặc  ở phía ngoài hình vuông ABCD dựng tam giác ABH đều.

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