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21-Nhã Lâm 7.8
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Nguyễn Lê Phước Thịnh
6 tháng 1 2022 lúc 9:54

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{b}{2}=\dfrac{c}{3}=\dfrac{b+c}{2+3}=\dfrac{130}{5}=26\)

Do đó: b=52; c=78

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Nguyễn Mai Nhan Ngọc
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Nguyễn Đức Anh
8 tháng 6 2016 lúc 10:36

A B C D E F I

a, 

ta có 

A + B+ C = \(180^0\)

B + C  = \(180^0\)-  A

mà BI là phân giác góc B

IBC = \(\frac{1}{2}\)B

CI là phân giác góc C 

ICB = \(\frac{1}{2}\)C

suy ra 

IBC + ICB = \(\frac{1}{2}\)B + \(\frac{1}{2}\)C = \(\frac{1}{2}\)( B + C ) = \(\frac{1}{2}\)\(180^0\)- A ) = \(\frac{1}{2}\) \(\left(180^0-60^0\right)\)\(60^0\)

mà IBC + ICB + BIC = \(180^0\)

suy ra BIC = \(180^0\)- ( IBC + ICB )

          BIC = \(180^0\)\(60^0\) 

          BIC = \(120^0\)

b,

ta có vì I là giao điểm của phân giác góc B và C 

suy ra phân giác góc A đi qua I suy ra tia AI trùng tia IF suy ra AF là phần giác góc A mà I cách đều AB ; AC ; BC 

nên IE = ID = IF

c,

ta có EIB + BIC =\(180^0\) 

       EIB = \(180^0-120^0\)

     EIB = \(60^0\)

    Mà EIB đối đỉnh góc DIC 

suy ra DIC = EIB =  \(60^0\)

vì IF là tia phân giác góc BIC 

nên BIF = CIF = \(\frac{1}{2}\)\(120^0\)\(60^0\)

EIF = BIE + BIF = \(60^0+60^0=120^0\)

DIF = DIC + CIF =  \(60^0+60^0=120^0\)

xét tam giác EIF và DIF có 

EIF = DIF = \(120^0\)

IF là cạnh chung 

IE = ID 

suy ra tam giác EIF = tam giác DIF ( c-g-c )

suy ra EF = DF 

ta có góc BIC đối đỉnh góc EID 

nên BIC = EID = \(120^0\)

xét tam giác EIF và EID có 

EID = EIF =\(120^0\)

ID = IF 

IE cạnh chung 

suy ra tam giác DIE = tam giác FIE ( c-g-c )

suy ra ED = EF 

mà EF = DF 

suy ra ED = EF = DF

suy ra tam giác EDF là tam giác đều 

d,

ta có IE = IF = ID 

nên I cách đều 3 đỉnh tam giác DFE nên I là giao điểm của 3 đường trung trực tam giác DEF 

mà trong tam giác đều 3 đường trung trực đồng thời là 3 đường phân giác của tam giác đó 

suy ra I là giao điểm của hai đường phân giác trong tam giác ABC vá DEF

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pham vo duy thuong
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TRAN HUU LOI
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Đào Khánh Huyền
11 tháng 7 2016 lúc 11:46

Ta có A,B,C tỉ lệ với 1,2,3

==>A/1=B/2=C/3

==> A+B+C/1+2+3=180ĐỘ/6=30 ĐỘ

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Nguyễn Hoàng
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Hung Nguyên kim
8 tháng 12 2021 lúc 20:08

-tổng 3 góc của 1 tam giác=180

-gọi ^A,^B,^C lần lượt là x,y,z

-áp dụng tính chất dãy tỉ số bằng nhau:

x/1=y/2=z/3=x+y+z/1+2+3=180/6=30

suy ra:x/1=30 suy ra x=30

suy ra:y/2=30 suy ra y=60

suy ra:z/3=30 suy ra z=90

suy ra ^A=30o;^B=60o;^C=90o

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My Hope
8 tháng 12 2021 lúc 20:34

Theo bài toán ta có:

\(\dfrac{A}{1}\)\(=\)\(\dfrac{B}{2}\)\(=\)\(\dfrac{C}{3}\) và A\(+\)B\(+\)C\(=\)180°(vì tổng ba góc của một tam giác bằng 180°)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\dfrac{A}{1}\)\(+\)\(\dfrac{B}{2}\)\(+\)\(\dfrac{C}{2}\)\(=\dfrac{A+B+C}{1+2+3}\)\(=\)\(\dfrac{180}{6}\)\(=\)30°

\(\Rightarrow\)\(\dfrac{A}{1}\)\(=\)30°. 1\(=\) 30°

    \(\dfrac{B}{2}\)\(=\) 30°. 2\(=\) 60°

     \(\dfrac{C}{3}\)\(=\)30°. 3\(=\)90°

Vậy số đo của ba góc A, B, C lần lượt là 30°, 60° và 90°

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Minh Bình
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Minh Bình
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Nguyễn Hoàng Minh
17 tháng 11 2021 lúc 7:11

Đề sai rồi bạn:

Nếu BK là p/g thì \(\widehat{B}=2\widehat{ABK}=220^0\)(vô lí)

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Trinh Hoàng
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Phan Huy Bằng
7 tháng 1 2022 lúc 8:34

B=60 độ

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Nguyễn Lê Phước Thịnh
7 tháng 1 2022 lúc 8:35

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{a+b+c}{2+3+4}=\dfrac{180}{9}=20\)

Do đó: b=60

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Nguyễn Tân Vương
7 tháng 1 2022 lúc 8:59

\(\text{Gọi x;y;z lần lượt là góc 1,góc 2,góc 3:}\)

          \(\text{ (đk:x;y;z>0,đơn vị:độ)}\)

\(\text{Ta có:}\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\text{ và }x+y+z=180^0\)

\(\text{Áp dụng tính chất dãy tỉ số bằng nhau:}\)

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}=\dfrac{180}{9}=20\)

\(\Rightarrow x=20.2=40^0\)

\(y=20.3=60^0\)

\(z=20.4=80^0\)

\(\text{Vậy số đo góc B là:}60^0\)

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

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