`a)` Ta có: `\hat{BAD}+\hat{ADC}=120^o +60^o =180^o`

    `=>a //// b` (Tổng `2` góc trong cùng phía bằng `180^o`)

`b)` Vì `a////b=>\hat{B}=\hat{BCD}` (`2` góc so le trong)

    `=>\hat{BCD}=55^o`

Theo đề ta có :

`x/3 = y/2; y/5 =z/3; x + y + z  =46`

`x/3 = y/2 => x/15 = y/10`

`y/5 = z/3 = y/10 = z/6`

`=> x/15 = y/10 = z/6`

Áp dụng tính chất dãy tính chất bằng nhau ta có :

`x/15 = y/10 = z/6 = (x+y+z)/(15+10+6) = 46/31`

`=>` \(\left\{{}\begin{matrix}\dfrac{x}{15}=\dfrac{46}{31}\times15=\dfrac{690}{31}\\\dfrac{y}{10}=\dfrac{46}{31}\times10=\dfrac{460}{31}\\\dfrac{z}{6}=\dfrac{46}{31}\times6=\dfrac{276}{31}\end{matrix}\right.\)

Vậy `x = 690/31; y= 460/31; z = 276/31`

x/3 = y/2 , y/5 = z/3

ta có: x/3 = x.5/ 3.5 = x/15 ; y/2= y.5/2.5 = y/10 ; y/5 = y.2/5.2 = y/10 ; z/3 = z.5/3.5= z/15

=>  x/15= y/10 ; y/10= z/15

=> x/15=y/10=z/15 , x+y+z = 46

=> x+y+z/ 15+10+15 = 46/40 = 1,15

=> y = 1,15 x 15 = 17,25

=> x = 1,15 x 10 = 11,5

=> z = 1,15 x 15 = 17,15 

`1/2. (x-1/3) + (-1)/2 = 3/4`

`1/2. (x-1/3)=3/4 - (-1/2)`

`1/2. (x-1/3)=3/4 + 1/2`

`1/2. (x-1/3)=3/4 + 2/4`

`1/2. (x-1/3)=5/4`

`x-1/3 = 5/4 : 1/2`

`x-1/3=5/4 xx 2`

`x-1/3 = 5/8`

`x=5/8+1/3`

`x=23/24`

__________________________

`4/5 -(x-1/6) = 2/3`

`x-1/6 =4/5 - 2/3`

`x-1/6 = 2/15`

`x=2/15 + 1/6`

`x=4/30 + 5/30`

`x=9/30`

`x=3/10`

_________________________

`|x + 1/3| - 4 = -1`

`|x +1/3| = -1 + 4`

`|x + 1/3 |  =3`

`@TH1:`

`x+1/3=3`

`x=3-1/3`

`x=9/3-1/3`

`x=8/3`

`@TH2:`

`x+1/3 = -3`

`x=-3-1/3`

`x=-9/3 - 1/3`

`x=-10/3`

Vậy `x = {8/3 ; -10/3}`

a) Ta thấy: \(\dfrac{3}{1^2.2^2}=\dfrac{2^2-1^2}{1^2.2^2}=1-\dfrac{1}{2^2}\)

\(\dfrac{5}{2^2.3^2}=\dfrac{3^2-2^2}{2^2.3^2}=\dfrac{1}{2^2}-\dfrac{1}{3^2}\)

\(\dfrac{7}{3^2.4^2}=\dfrac{4^2-3^2}{3^2.4^2}=\dfrac{1}{3^2}-\dfrac{1}{4^2}\)

...

\(\dfrac{19}{9^2.10^2}=\dfrac{10^2-9^2}{9^2.10^2}=\dfrac{1}{9^2}-\dfrac{1}{10^2}\)

Từ đó, ta có \(S=1-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+\dfrac{1}{3^2}-\dfrac{1}{4^2}+...+\dfrac{1}{9^2}-\dfrac{1}{10^2}\)

\(S=1-\dfrac{1}{10^2}\)

\(S=\dfrac{99}{100}\)

b) Mình suy nghĩ sau nhé

Không bạn nhé. Hai tam giác đó chị đồng dạng với nhau thôi.

Bạn thử vẽ tam giác có các cạnh là `3, 4,5 ; 6, 8, 10` xem chúng có góc bằng nhau không nha.